The N Implementation Details of RLHF with PPO
Shengyi Costa Huang, Tianlin Liu, Leandro von Werra
RLHF / ChatGPT has been a popular research topic these days. In our quest to research more on RLHF, this blog post attempts to do a reproduction of OpenAI’s 2019 original RLHF codebase at openai/lm-human-preferences. Despite its “tensorflow-1.x-ness,” OpenAI’s original codebase is very well-evaluated and benchmarked, making it a good place to study RLHF implementation engineering details.We aim to:reproduce OAI’s results in stylistic tasks and match the learning curves of openai/lm-human-preferences. present a checklist of implementation details, similar to the spirit of The 37 Implementation Details of Proximal Policy Optimization; Debugging RL, Without the Agonizing Pain.provide a simple-to-read and minimal reference implementation of RLHF;This work is just for educational / learning purposes. For advanced users requiring more features, such as running larger models with PEFT, huggingface/trl would be a great choice.In Matching Learning Curves, we show our main contribution: creating a codebase that can reproduce OAI’s results in the stylistic tasks and matching learning curves very closely with openai/lm-human-preferences.We then take a technical deep dive into the implementation details that are relevant to reproducing OAI’s work. In General Implementation Details, we talk about basic details, such as how rewards/values are generated and how responses are generated. In Reward Model Implementation Details, we talk about details such as reward normalization. In Policy Training Implementation Details, we discuss details such as rejection sampling and reward “whitening”.In PyTorch Adam optimizer numerical issues w.r.t RLHF, we highlight a very interesting implementation difference in Adam between TensorFlow and PyTorch, which causes an aggressive update in the model training.Next, we examine the effect of training different base models (e.g., gpt2-xl, falcon-1b,) given that the reward labels are produced with gpt2-large.Finally, we conclude our work with limitations and discussions.Here are the important links:💾 Our reproduction codebase https://github.com/vwxyzjn/lm-human-preference-details🤗 Demo of RLHF model comparison: https://huggingface.co/spaces/lm-human-preference-details/rlhf-demo🐝 All w&b training logs https://wandb.ai/openrlbenchmark/lm_human_preference_details		Matching Learning Curves	Our main contribution is to reproduce OAI’s results in stylistic tasks, such as sentiment and descriptiveness. As shown in the figure below, our codebase (orange curves) can produce nearly identical learning curves as OAI’s codebase (blue curves).		A note on running openai/lm-human-preferences	To make a direct comparison, we ran the original RLHF code at openai/lm-human-preferences, which will offer valuable metrics to help validate and diagnose our reproduction. We were able to set the original TensorFlow 1.x code up, but it requires a hyper-specific setup:OAI’s dataset was partially corrupted/lost (so we replaced them with similar HF datasets, which may or may not cause a performance difference)Specifically, its book dataset was lost during OpenAI’s GCP - Azure migration (https://github.com/openai/lm-human-preferences/issues/17#issuecomment-1044051496). I replaced the book dataset with Hugging Face’s bookcorpus dataset, which is, in principle, what OAI used.It can’t run on 1 V100 because it doesn’t implement gradient accumulation. Instead, it uses a large batch size and splits the batch across 8 GPUs, and will OOM on just 1 GPU.It can’t run on 8x A100 because it uses TensorFlow 1.x, which is incompatible with Cuda 8+It can’t run on 8x V100 (16GB) because it will OOMIt can only run on 8x V100 (32GB), which is only offered by AWS as the p3dn.24xlarge instance.		General Implementation Details	We now take a technical deep dive into the implementation details that are relevant to reproducing OAI’s work. In this section, we talk about basic details, such as how rewards/values are generated and how responses are generated. Here are these details in no particular order:The reward model and policy’s value head take input as the concatenation of query and responseThe reward model and policy’s value head do not only look at the response. Instead, it concatenates the query and response together as query_response (lm_human_preferences/rewards.py#L105-L107).So, for example, if query = "he was quiet for a minute, his eyes unreadable"., and the response = "He looked at his left hand, which held the arm that held his arm out in front of him.", then the reward model and policy’s value do a forward pass on query_response = "he was quiet for a minute, his eyes unreadable. He looked at his left hand, which held the arm that held his arm out in front of him." and produced rewards and values of shape (B, T, 1), where B is the batch size, T is the sequence length, and 1 is the reward head dimension of 1 (lm_human_preferences/rewards.py#L105-L107, lm_human_preferences/policy.py#L111). The T means that each token has a reward associated with it and its previous context. For example, the eyes token would have a reward corresponding to he was quiet for a minute, his eyes.Pad with a special padding token and truncate inputs. OAI sets a fixed input length for query query_length; it pads sequences that are too short with pad_token (lm_human_preferences/language/datasets.py#L66-L67) and truncates sequences that are too long (lm_human_preferences/language/datasets.py#L57). See here for a general introduction to the concept). When padding the inputs, OAI uses a token beyond the vocabulary (lm_human_preferences/language/encodings.py#L56).Note on HF’s transformers — padding token. According to  (transformers#2630#issuecomment-578159876), padding tokens were not used during the pre-training of GPT and GPT-2; therefore transformer’s gpt2 models have no official padding token associated with its tokenizer. A common practice is to set tokenizer.pad_token = tokenizer.eos_token, but in this work, we shall distinguish these two special tokens to match OAI’s original setting, so we will use tokenizer.add_special_tokens({"pad_token": "[PAD]"}). Note that having no padding token is a default setting for decoder models, since they train with “packing” during pretraining, which means that many sequences are concatenated and separated by the EOS token and chunks of this sequence that always have the max length are fed to the model during pretraining.When putting everything together, here is an exampleimport transformerstokenizer = transformers.AutoTokenizer.from_pretrained("gpt2", padding_side="right")tokenizer.add_special_tokens({"pad_token": "[PAD]"})query_length = 5texts = [    "usually, he would",    "she thought about it",]    tokens = []for text in texts:    tokens.append(tokenizer.encode(text)[:query_length])print("tokens", tokens)inputs = tokenizer.pad(    {"input_ids": tokens},    padding="max_length",    max_length=query_length,    return_tensors="pt",    return_attention_mask=True,)print("inputs", inputs)"""prints aretokens [[23073, 11, 339, 561], [7091, 1807, 546, 340]]inputs {'input_ids': tensor([[23073,    11,   339,   561, 50257],        [ 7091,  1807,   546,   340, 50257]]), 'attention_mask': tensor([[1, 1, 1, 1, 0],        [1, 1, 1, 1, 0]])}"""Adjust position indices correspondingly for padding tokensWhen calculating the logits, OAI’s code works by masking out padding tokens properly. This is achieved by finding out the token indices corresponding to the padding tokens (lm_human_preferences/language/model.py#L296-L297), followed by adjusting their position indices correspondingly (lm_human_preferences/language/model.py#L320).For example, if the query=[23073, 50259, 50259] and response=[11, 339, 561], where (50259 is OAI’s padding token), it then creates position indices as [[0 1 1 1 2 3]] and logits as follows. Note how the logits corresponding to the padding tokens remain the same as before! This is the effect we should be aiming for in our reproduction.all_logits [[[ -35.28693   -34.2875    -38.16074  ...  -41.595802  -41.082108    -35.36577 ]  [ -35.28693   -34.2875    -38.16074  ...  -41.595802  -41.082108    -35.36577 ]  [ -35.28693   -34.2875    -38.16074  ...  -41.595802  -41.082108    -35.36577 ]  [-111.303955 -110.94471  -112.90624  ... -113.13064  -113.7788   -109.17345 ]  [-111.51512  -109.61077  -114.90231  ... -118.43514  -111.56671   -112.12478 ]  [-122.69775  -121.84468  -128.27417  ... -132.28055  -130.39604   -125.707756]]] (1, 6, 50257)Note on HF’s transformers — position_ids and padding_side. We can replicate the exact logits using Hugging Face’s transformer with 1) left padding and 2) pass in the appropriate position_ids:import torchimport transformerstokenizer = transformers.AutoTokenizer.from_pretrained("gpt2", padding_side="right")tokenizer.add_special_tokens({"pad_token": "[PAD]"})pad_id = tokenizer.pad_token_idquery = torch.tensor([    [pad_id, pad_id, 23073],])response = torch.tensor([    [11, 339, 561],])temperature = 1.0query = torch.tensor(query)response = torch.tensor(response).long()context_length = query.shape[1]query_response = torch.cat((query, response), 1)pretrained_model = transformers.AutoModelForCausalLM.from_pretrained("gpt2")def forward(policy, query_responses, tokenizer):    attention_mask = query_responses != tokenizer.pad_token_id    position_ids = attention_mask.cumsum(1) - attention_mask.long()  # exclusive cumsum    input_ids = query_responses.clone()    input_ids[~attention_mask] = 0    return policy(        input_ids=input_ids,        attention_mask=attention_mask,        position_ids=position_ids,        return_dict=True,        output_hidden_states=True,    )output = forward(pretrained_model, query_response, tokenizer)logits = output.logitslogits /= temperatureprint(logits)"""tensor([[[ -26.9395,  -26.4709,  -30.0456,  ...,  -33.2208,  -33.2884,           -27.4360],         [ -27.1677,  -26.7330,  -30.2386,  ...,  -33.6813,  -33.6931,           -27.5928],         [ -35.2869,  -34.2875,  -38.1608,  ...,  -41.5958,  -41.0821,           -35.3658],         [-111.3040, -110.9447, -112.9062,  ..., -113.1306, -113.7788,          -109.1734],         [-111.5152, -109.6108, -114.9024,  ..., -118.4352, -111.5668,          -112.1248],         [-122.6978, -121.8447, -128.2742,  ..., -132.2805, -130.3961,          -125.7078]]], grad_fn=<DivBackward0>)"""Note on HF’s transformers — position_ids during generate: during generate we should not pass in position_ids because the position_ids are already adjusted in transformers (see huggingface/transformers#/7552. Usually, we almost never pass position_ids in transformers. All the masking and shifting logic are already implemented e.g. in the generate function (need permanent code link).Response generation samples a fixed-length response without padding.During response generation, OAI uses top_k=0, top_p=1.0 and just do categorical samples across the vocabulary  (lm_human_preferences/language/sample.py#L43) and the code would keep sampling until a fixed-length response is generated (lm_human_preferences/policy.py#L103). Notably, even if it encounters EOS (end-of-sequence) tokens, it will keep sampling.Note on HF’s transformers — sampling could stop at eos_token: in transformers, the generation could stop at eos_token (src/transformers/generation/utils.py#L2248-L2256), which is not the same as OAI’s setting. To align the setting, we need to do set pretrained_model.generation_config.eos_token_id = None, pretrained_model.generation_config.pad_token_id = None. Note that transformers.GenerationConfig(eos_token_id=None, pad_token_id=None, ...) does not work because pretrained_model.generation_config would override and set a eos_token.import torchimport transformerstokenizer = transformers.AutoTokenizer.from_pretrained("gpt2", padding_side="right")tokenizer.add_special_tokens({"pad_token": "[PAD]"})pad_id = tokenizer.pad_token_idquery = torch.tensor([    [pad_id, pad_id, 23073],])response = torch.tensor([    [11, 339, 561],])response_length = 4temperature = 0.7pretrained_model = transformers.AutoModelForCausalLM.from_pretrained("gpt2")pretrained_model.generation_config.eos_token_id = None # disable `pad_token_id` and `eos_token_id` because we just want topretrained_model.generation_config.pad_token_id = None  # generate tokens without truncation / paddinggeneration_config = transformers.GenerationConfig(    max_new_tokens=response_length,    min_new_tokens=response_length,    temperature=temperature,    top_k=0.0,    top_p=1.0,    do_sample=True,)context_length = query.shape[1]attention_mask = query != tokenizer.pad_token_idinput_ids = query.clone()input_ids[~attention_mask] = 0  # set padding tokens to 0output = pretrained_model.generate(    input_ids=input_ids,    attention_mask=attention_mask,    # position_ids=attention_mask.cumsum(1) - attention_mask.long(), # generation collapsed if this was turned on.    generation_config=generation_config,    return_dict_in_generate=True,)print(output.sequences)"""tensor([[    0,     0, 23073, 16851,    11,   475,   991]])"""Note that in a more recent codebase https://github.com/openai/summarize-from-feedback, OAI does stop sampling when encountering EOS token (summarize_from_feedback/utils/experiment_helpers.py#L19). However in this work we aim to do a 1:1 replication, so we align the setting that could keep sampling even eos_token is encounteredLearning rate annealing for reward model and policy training.As Ziegler et al. (2019) suggested, the reward model is trained for a single epoch to avoid overfitting the limited amount of human annotation data (e.g., the descriptiveness task only had about 5000 labels). During this single epoch, the learning rate is annealed to zero (lm_human_preferences/train_reward.py#L249).Similar to reward model training, the learning rate is annealed to zero (lm_human_preferences/train_policy.py#L172-L173).Use different seeds for different processesWhen spawning 8 GPU processes to do data parallelism, OAI sets a different random seed per process (lm_human_preferences/utils/core.py#L108-L111). Implementation-wise, this is done via local_seed = args.seed + process_rank * 100003. The seed is going to make the model produce different responses and get different scores, for example.Note: I believe the dataset shuffling has a bug — the dataset is shuffled using the same seed for some reason (lm_human_preferences/lm_tasks.py#L94-L97).		Reward Model Implementation Details	In this section, we discuss reward-model-specific implementation details. We talk about details such as reward normalization and layer initialization. Here are these details in no particular order:The reward model only outputs the value at the last token.Notice that the rewards obtained after the forward pass on the concatenation of query and response will have the shape (B, T, 1), where B is the batch size, T is the sequence length (which is always the same; it is query_length + response_length = 64 + 24 = 88 in OAI’s setting for stylistic tasks, see launch.py#L9-L11), and 1 is the reward head dimension of 1.  For RLHF purposes, the original codebase extracts the reward of the last token (lm_human_preferences/rewards.py#L132), so that the rewards will only have shape (B, 1). Note that in a more recent codebase openai/summarize-from-feedback, OAI stops sampling when encountering EOS token (summarize_from_feedback/utils/experiment_helpers.py#L19). When extracting rewards, it is going to identify the last_response_index, the index before the EOS token (#L11-L13), and extract the reward at that index (summarize_from_feedback/reward_model.py#L59). However in this work we just stick with the original setting.Reward head layer initializationThe weight of the reward head is initialized according to N(0,1/(dmodel +1)) \mathcal{N}\left(0,1 /\left(\sqrt{d_{\text {model }}+1}\right)\right) N(0,1/(dmodel ​+1​)) (lm_human_preferences/language/model.py#L368, lm_human_preferences/language/model.py#L251-L252). This aligns with the settings in  Stiennon et al., 2020 (summarize_from_feedback/query_response_model.py#L106-L107) (P.S., Stiennon et al., 2020 had a typo on page 17 saying the distribution is  N(0,1/(dmodel +1)) \mathcal{N}\left(0,1 /\left(d_{\text {model }}+1\right)\right) N(0,1/(dmodel ​+1)) without the square root)The bias of the reward head is set to 0 (lm_human_preferences/language/model.py#L254).Reward model normalization before and afterIn the paper, Ziegler el al. (2019) mentioned that "to keep the scale of the reward model consistent across training, we normalize it so that it has mean 0 and variance 1 for x∼D,y∼ρ(⋅∣x) x \sim \mathcal{D}, y \sim \rho(·|x) x∼D,y∼ρ(⋅∣x).” To perform the normalization process, the code first creates a reward_gain and reward_bias, such that the reward can be calculated by reward = reward * reward_gain + reward_bias (lm_human_preferences/rewards.py#L50-L51). When performing the normalization process, the code first sets reward_gain=1, reward_bias=0 (lm_human_preferences/train_reward.py#L211), followed by collecting sampled queries from the target dataset (e.g., bookcorpus, tldr, cnndm), completed responses, and evaluated rewards. It then gets the empirical mean and std of the evaluated reward (lm_human_preferences/train_reward.py#L162-L167) and tries to compute what the reward_gain and reward_bias should be. Let us use μD \mu_{\mathcal{D}} μD​ to denote the empirical mean, σD \sigma_{\mathcal{D}} σD​ the empirical std, ggg the reward_gain, bbb reward_bias,  μT=0 \mu_{\mathcal{T}} = 0μT​=0 target mean and σT=1 \sigma_{\mathcal{T}}=1σT​=1 target std. Then we have the following formula. g∗N(μD,σD)+b=N(g∗μD,g∗σD)+b=N(g∗μD+b,g∗σD)=N(μT,σT)g=σTσDb=μT−g∗μD\begin{aligned}g*\mathcal{N}(\mu_{\mathcal{D}}, \sigma_{\mathcal{D}}) + b &= \mathcal{N}(g*\mu_{\mathcal{D}}, g*\sigma_{\mathcal{D}}) + b\\&= \mathcal{N}(g*\mu_{\mathcal{D}} + b, g*\sigma_{\mathcal{D}}) \\&= \mathcal{N}(\mu_{\mathcal{T}}, \sigma_{\mathcal{T}}) \\g &= \frac{\sigma_{\mathcal{T}}}{\sigma_{\mathcal{D}}} \\b &= \mu_{\mathcal{T}} - g*\mu_{\mathcal{D}}\end{aligned}g∗N(μD​,σD​)+bgb​=N(g∗μD​,g∗σD​)+b=N(g∗μD​+b,g∗σD​)=N(μT​,σT​)=σD​σT​​=μT​−g∗μD​​The normalization process is then applied before and after reward model training (lm_human_preferences/train_reward.py#L232-L234, lm_human_preferences/train_reward.py#L252-L254).Note that responses  y∼ρ(⋅∣x) y \sim \rho(·|x) y∼ρ(⋅∣x) we generated for the normalization purpose are from the pre-trained language model ρ\rho ρ. The model ρ\rho ρ  is fixed as a reference and is not updated in reward learning (lm_human_preferences/train_reward.py#L286C1-L286C31).		Policy Training Implementation Details	In this section, we will delve into details, such as layer initialization, data post-processing, and dropout settings. We will also explore techniques, such as of rejection sampling and reward "whitening", and adaptive KL. Here are these details in no particular order:Scale the logits by sampling temperature. When calculating the log probability of responses, the model first outputs the logits of the tokens in the responses, followed by dividing the logits with the sampling temperature (lm_human_preferences/policy.py#L121). I.e., logits /= self.temperatureIn an informal test, we found that without this scaling, the KL would rise faster than expected, and performance would deteriorate.Value head layer initializationThe weight of the value head is initialized according to N(0,0)\mathcal{N}\left(0,0\right)N(0,0) (lm_human_preferences/language/model.py#L368, lm_human_preferences/language/model.py#L251-L252). This is The bias of the reward head is set to 0 (lm_human_preferences/language/model.py#L254).Select query texts that start and end with a periodThis is done as part of the data preprocessing;Tries to select text only after start_text="." (lm_human_preferences/language/datasets.py#L51)Tries select text just before end_text="." (lm_human_preferences/language/datasets.py#L61)Then pad the text (lm_human_preferences/language/datasets.py#L66-L67)When running openai/lm-human-preferences, OAI’s datasets were partially corrupted/lost (openai/lm-human-preferences/issues/17#issuecomment-104405149), so we had to replace them with similar HF datasets, which may or may not cause a performance difference) For the book dataset, we used https://huggingface.co/datasets/bookcorpus, which we find not necessary to extract sentences that start and end with periods because the dataset ) is already pre-processed this way (e.g., "usually , he would be tearing around the living room , playing with his toys .") To this end, we set start_text=None, end_text=None for the sentiment and descriptiveness tasks.Disable dropoutZiegler et al. (2019) suggested, “We do not use dropout for policy training.” This is also done in the code (lm_human_preferences/policy.py#L48).Rejection sampling Ziegler et al. (2019) suggested, “We use rejection sampling to ensure there is a period between tokens 16 and 24 and then truncate at that period (This is a crude approximation for ‘end of sentence.’ We chose it because it is easy to integrate into the RL loop, and even a crude approximation is sufficient for the intended purpose of making the human evaluation task somewhat easier). During the RL finetuning, we penalize continuations that don’t have such a period by giving them a fixed reward of −1.”Specifically, this is achieved with the following steps:Token truncation: We want to truncate at the first occurrence of truncate_token that appears at or after position truncate_after in the responses (lm_human_preferences/train_policy.py#L378)Code comment: “central example: replace all tokens after truncate_token with padding_token”Run reward model on truncated response: After the response has been truncated by the token truncation process, the code then runs the reward model on the truncated response.Rejection sampling: if there is not a period between tokens 16 and 24, then replace the score of the response with a fixed low value (such as -1)(lm_human_preferences/train_policy.py#L384, lm_human_preferences/train_policy.py#L384-L402)Code comment: “central example: ensure that the sample contains truncate_token"Code comment:  “only query humans on responses that pass that function“To give some examples in descriptiveness:  Samples extracted from our reproduction https://wandb.ai/openrlbenchmark/lm_human_preference_details/runs/djf8yymv/logs. Notice the 1st and 3rd example has too many tokens after the period, so its score was replaced by -1.Discount factor = 1The discount parameter γ\gammaγ is set to 1 (lm_human_preferences/train_policy.py#L56), which means that future rewards are given the same weight as immediate rewards.Terminology of the training loop: batches and minibatches in PPOOAI uses the following training loop (lm_human_preferences/train_policy.py#L184-L192). Note: we additionally added the micro_batch_size to help deal with the case in gradient accumulation. At each epoch, it shuffles the batch indices.import numpy as npbatch_size = 8nminibatches = 2gradient_accumulation_steps = 2mini_batch_size = batch_size // nminibatchesmicro_batch_size = mini_batch_size // gradient_accumulation_stepsdata = np.arange(batch_size).astype(np.float32)print("data:", data)print("batch_size:", batch_size)print("mini_batch_size:", mini_batch_size)print("micro_batch_size:", micro_batch_size)for epoch in range(4):    batch_inds = np.random.permutation(batch_size)    print("epoch:", epoch, "batch_inds:", batch_inds)    for mini_batch_start in range(0, batch_size, mini_batch_size):        mini_batch_end = mini_batch_start + mini_batch_size        mini_batch_inds = batch_inds[mini_batch_start:mini_batch_end]                # `optimizer.zero_grad()` set optimizer to zero for gradient accumulation        for micro_batch_start in range(0, mini_batch_size, micro_batch_size):            micro_batch_end = micro_batch_start + micro_batch_size             micro_batch_inds = mini_batch_inds[micro_batch_start:micro_batch_end]            print("____⏩ a forward pass on", data[micro_batch_inds])        # `optimizer.step()`        print("⏪ a backward pass on", data[mini_batch_inds])# data: [0. 1. 2. 3. 4. 5. 6. 7.]# batch_size: 8# mini_batch_size: 4# micro_batch_size: 2# epoch: 0 batch_inds: [6 4 0 7 3 5 1 2]# ____⏩ a forward pass on [6. 4.]# ____⏩ a forward pass on [0. 7.]# ⏪ a backward pass on [6. 4. 0. 7.]# ____⏩ a forward pass on [3. 5.]# ____⏩ a forward pass on [1. 2.]# ⏪ a backward pass on [3. 5. 1. 2.]# epoch: 1 batch_inds: [6 7 3 2 0 4 5 1]# ____⏩ a forward pass on [6. 7.]# ____⏩ a forward pass on [3. 2.]# ⏪ a backward pass on [6. 7. 3. 2.]# ____⏩ a forward pass on [0. 4.]# ____⏩ a forward pass on [5. 1.]# ⏪ a backward pass on [0. 4. 5. 1.]# epoch: 2 batch_inds: [1 4 5 6 0 7 3 2]# ____⏩ a forward pass on [1. 4.]# ____⏩ a forward pass on [5. 6.]# ⏪ a backward pass on [1. 4. 5. 6.]# ____⏩ a forward pass on [0. 7.]# ____⏩ a forward pass on [3. 2.]# ⏪ a backward pass on [0. 7. 3. 2.]# epoch: 3 batch_inds: [7 2 4 1 3 0 6 5]# ____⏩ a forward pass on [7. 2.]# ____⏩ a forward pass on [4. 1.]# ⏪ a backward pass on [7. 2. 4. 1.]# ____⏩ a forward pass on [3. 0.]# ____⏩ a forward pass on [6. 5.]# ⏪ a backward pass on [3. 0. 6. 5.]Per-token KL penaltyThe code adds a per-token KL penalty (lm_human_preferences/train_policy.py#L150-L153) to the rewards, in order to discourage the policy to be very different from the original policy.Using the "usually, he would" as an example, it gets tokenized to [23073, 11, 339, 561]. Say we use [23073] as the query and [11, 339, 561] as the response. Then under the default gpt2 parameters, the response tokens will have log probabilities of the reference policy logprobs=[-3.3213, -4.9980, -3.8690] .During the first PPO update epoch and minibatch update, so the active policy will have the same log probabilities new_logprobs=[-3.3213, -4.9980, -3.8690]. , so the per-token KL penalty would be  kl = new_logprobs - logprobs = [0., 0., 0.,]However, after the first gradient backward pass, we could have new_logprob=[3.3213, -4.9980, -3.8690] , so the per-token KL penalty becomes kl = new_logprobs - logprobs = [-0.3315, -0.0426, 0.6351]Then the non_score_reward = beta * kl , where beta is the KL penalty coefficient  β\betaβ, and it’s added to the score obtained from the reward model to create the rewards used for training. The score is only given at the end of episode; it could look like [0.4,] , and we have rewards = [beta * -0.3315, beta * -0.0426, beta * 0.6351 + 0.4].Per-minibatch reward and advantage whitening, with optional mean shiftingOAI implements a whiten function that looks like below, basically normalizing the values by subtracting its mean followed by dividing by its standard deviation. Optionally, whiten can shift back the mean of the whitened values with shift_mean=True.def whiten(values, shift_mean=True):    mean, var = torch.mean(values), torch.var(values, unbiased=False)    whitened = (values - mean) * torch.rsqrt(var + 1e-8)    if not shift_mean:        whitened += mean    return whitenedIn each minibatch, OAI then whitens the reward whiten(rewards, shift_mean=False) without shifting the mean (lm_human_preferences/train_policy.py#L325) and whitens the advantages whiten(advantages) with the shifted mean (lm_human_preferences/train_policy.py#L338).Optimization note: if the number of minibatches is one (which is the case in this reproduction) we only need to whiten rewards, calculate and whiten advantages once since their values won’t change.TensorFlow vs PyTorch note: Different behavior of tf.moments vs torch.var: The behavior of whitening is different in torch vs tf because the variance calculation is different: import numpy as npimport tensorflow as tfimport torchdef whiten_tf(values, shift_mean=True):    mean, var = tf.nn.moments(values, axes=list(range(values.shape.rank)))    mean = tf.Print(mean, [mean], 'mean', summarize=100)    var = tf.Print(var, [var], 'var', summarize=100)    whitened = (values - mean) * tf.rsqrt(var + 1e-8)    if not shift_mean:        whitened += mean    return whiteneddef whiten_pt(values, shift_mean=True, unbiased=True):    mean, var = torch.mean(values), torch.var(values, unbiased=unbiased)    print("mean", mean)    print("var", var)    whitened = (values - mean) * torch.rsqrt(var + 1e-8)    if not shift_mean:        whitened += mean    return whitenedrewards = np.array([    [1.2, 1.3, 1.4],    [1.5, 1.6, 1.7],    [1.8, 1.9, 2.0],])with tf.Session() as sess:    print(sess.run(whiten_tf(tf.constant(rewards, dtype=tf.float32), shift_mean=False)))    print(whiten_pt(torch.tensor(rewards), shift_mean=False, unbiased=True))    print(whiten_pt(torch.tensor(rewards), shift_mean=False, unbiased=False))mean[1.5999999]var[0.0666666627][[0.05080712 0.4381051  0.8254035 ] [1.2127019  1.6000004  1.9872988 ] [2.3745968  2.7618952  3.1491938 ]]mean tensor(1.6000, dtype=torch.float64)var tensor(0.0750, dtype=torch.float64)tensor([[0.1394, 0.5046, 0.8697],        [1.2349, 1.6000, 1.9651],        [2.3303, 2.6954, 3.0606]], dtype=torch.float64)mean tensor(1.6000, dtype=torch.float64)var tensor(0.0667, dtype=torch.float64)tensor([[0.0508, 0.4381, 0.8254],        [1.2127, 1.6000, 1.9873],        [2.3746, 2.7619, 3.1492]], dtype=torch.float64)Clipped value functionAs done in the original PPO (baselines/ppo2/model.py#L68-L75), the value function is clipped (lm_human_preferences/train_policy.py#L343-L348) in a similar fashion as the policy objective.Adaptive KLThe KL divergence penalty coefficient β\betaβ is modified adaptively based on the KL divergence between the current policy and the previous policy. If the KL divergence is outside a predefined target range, the penalty coefficient is adjusted to bring it closer to the target range (lm_human_preferences/train_policy.py#L115-L124). It’s implemented as follows:class AdaptiveKLController:    def __init__(self, init_kl_coef, hparams):        self.value = init_kl_coef        self.hparams = hparams    def update(self, current, n_steps):        target = self.hparams.target        proportional_error = np.clip(current / target - 1, -0.2, 0.2)        mult = 1 + proportional_error * n_steps / self.hparams.horizon        self.value *= multFor the sentiment and descriptiveness tasks examined in this work, we have init_kl_coef=0.15, hparams.target=6, hparams.horizon=10000.PyTorch Adam optimizer numerical issues w.r.t RLHFThis implementation detail is so interesting that it deserves a full section.PyTorch Adam optimizer (torch.optim.Adam.html) has a different implementation compared to TensorFlow’s Adam optimizer (TF1 Adam at tensorflow/v1.15.2/adam.py, TF2 Adam at keras/adam.py#L26-L220). In particular, PyTorch follows Algorithm 1 of the Kingma and Ba’s Adam paper (arxiv/1412.6980), but TensorFlow uses the formulation just before Section 2.1 of the paper and its epsilon referred to here is epsilon hat in the paper. In a pseudocode comparison, we have the following### pytorch adam implementation:bias_correction1 = 1 - beta1 ** stepbias_correction2 = 1 - beta2 ** stepstep_size = lr / bias_correction1bias_correction2_sqrt = _dispatch_sqrt(bias_correction2)denom = (exp_avg_sq.sqrt() / bias_correction2_sqrt).add_(eps)param.addcdiv_(exp_avg, denom, value=-step_size)### tensorflow adam implementation:lr_t = lr * _dispatch_sqrt((1 - beta2 ** step)) / (1 - beta1 ** step)denom = exp_avg_sq.sqrt().add_(eps)param.addcdiv_(exp_avg, denom, value=-lr_t)Let’s compare the update equations of pytorch-style and tensorflow-style adam. Following the notation of the adam paper (Kingma and Ba, 2014),  we have the gradient update rules for pytorch adam (Algorithm 1 of Kingma and Ba’s paper) and tensorflow-style adam (the formulation just before Section 2.1 of Kingma and Ba’s paper) as below:pytorch adam :θt=θt−1−α⋅m^t/(v^t+ε)=θt−1−α[mt/(1−β1t)]⏟=m^t/[vt/(1−β2t)⏟=v^t+ε]=θt−1−α[mt/(1−β1t)]1−β2tvt+ε1−β2t\begin{aligned}\text{pytorch adam :}\quad \theta_t & =\theta_{t-1}-\alpha \cdot \hat{m}_t /\left(\sqrt{\hat{v}_t}+\varepsilon\right) \\& =\theta_{t-1}- \alpha \underbrace{\left[m_t /\left(1-\beta_1^t\right)\right]}_{=\hat{m}_t} /\left[\sqrt{\underbrace{v_t /\left(1-\beta_2^t\right)}_{=\hat{v}_t} }+\varepsilon\right]\\& =\theta_{t-1}- \alpha\left[m_t /\left(1-\beta_1^t\right)\right]\frac{\sqrt{1-\beta_2^t}}{\sqrt{v_t}+\color{green}{\varepsilon \sqrt{1-\beta_2^t}}}\end{aligned}pytorch adam :θt​​=θt−1​−α⋅m^t​/(v^t​​+ε)=θt−1​−α=m^t​[mt​/(1−β1t​)]​​/​=v^t​vt​/(1−β2t​)​​​+ε​=θt−1​−α[mt​/(1−β1t​)]vt​​+ε1−β2t​​1−β2t​​​​tensorflow adam:θt=θt−1−αtmt/(vt+ε^)=θt−1−[α1−β2t/(1−β1t)]⏟=αtmt/(vt+ε^)=θt−1−α[mt/(1−β1t)]1−β2tvt+ε^\begin{aligned}\text{tensorflow adam:}\quad \theta_t & =\theta_{t-1}-\alpha_t m_t /\left(\sqrt{v_t}+\hat{\varepsilon}\right) \\& =\theta_{t-1}-\underbrace{\left[\alpha \sqrt{1-\beta_2^t} /\left(1-\beta_1^t\right)\right]}_{=\alpha_t} m_t /\left(\sqrt{v_t}+\hat{\varepsilon}\right) \\& =\theta_{t-1}- \alpha\left[m_t /\left(1-\beta_1^t\right)\right] \frac{\sqrt{1-\beta_2^t}}{\sqrt{v_t}+\color{green}{\hat{\varepsilon}}} \end{aligned}tensorflow adam:θt​​=θt−1​−αt​mt​/(vt​​+ε^)=θt−1​−=αt​[α1−β2t​​/(1−β1t​)]​​mt​/(vt​​+ε^)=θt−1​−α[mt​/(1−β1t​)]vt​​+ε^1−β2t​​​​The equations above highlight that the distinction between pytorch and tensorflow implementation is their normalization terms, ε1−β2t\color{green}{\varepsilon \sqrt{1-\beta_2^t}}ε1−β2t​​  and ε^\color{green}{\hat{\varepsilon}}ε^. The two versions are equivalent if we set  ε^=ε1−β2t\hat{\varepsilon}  =\varepsilon \sqrt{1-\beta_2^t}ε^=ε1−β2t​​ .  However, in the pytorch and tensorflow APIs, we can only set ε\varepsilonε (pytorch) and ε^\hat{\varepsilon}ε^ (tensorflow) via the eps argument, causing differences in their update equations. What if we set  ε\varepsilonε and ε^\hat{\varepsilon}ε^  to the same value, say, 1e-5? Then for tensorflow adam, the normalization term ε^=1e-5\hat{\varepsilon} = \text{1e-5}ε^=1e-5  is just a constant. But for pytorch adam, the normalization term ε1−β2t{\varepsilon \sqrt{1-\beta_2^t}}ε1−β2t​​ changes over time. Importantly, initially much smaller than 1e-5 when the timestep ttt is small, the term  ε1−β2t{\varepsilon \sqrt{1-\beta_2^t}}ε1−β2t​​  gradually approaches to 1e-5 as timesteps increase. The plot below compares these two normalization terms over timesteps: The above figure shows that, if we set the same eps in pytorch adam and tensorflow adam, then pytorch-adam uses a much smaller normalization term than tensorflow-adam in the early phase of training. In other words, pytorch adam goes for more aggressive gradient updates early in the training. Our experiments support this finding, as we will demonstrate below.How does this impact reproducibility and performance? To align settings, we record the original query, response, and rewards from https://github.com/openai/lm-human-preferences and save them in https://huggingface.co/datasets/vwxyzjn/lm-human-preferences-debug/tree/main. I also record the metrics of the first two epochs of training with TF1’s AdamOptimizer optimizer as the ground truth.  Below are some key metrics:OAI’s TF1 AdamPyTorch’s AdamOur custom Tensorflow-style Adampolicy/approxkl0.000371670230.00236728345043957230.000374998344341293policy/clipfrac0.00455729150.020182291045784950.0052083334885537624ratio_mean1.00512851.01055204868316651.0044583082199097ratio_var0.00077165460.0053742756135761740.0007942612282931805ratio_max1.2272161.81210577487945561.250215768814087ratio_min0.74004410.40113878250122070.7299948930740356logprob_diff_mean0.00474876030.0081012519076466560.004073789343237877logprob_diff_var0.00072078970.0046689365990459920.0007334011606872082logprob_diff_max0.204748210.5944895744323730.22331619262695312logprob_diff_min-0.30104542-0.9134478569030762-0.31471776962280273PyTorch’s Adam produces a more aggressive update for some reason. Here are some evidence:PyTorch’s Adam's logprob_diff_var is 6x higher. Here logprobs_diff = new_logprobs - logprobs is the difference between the log probability of tokens between the initial and current policy after two epochs of training. Having a larger logprob_diff_var means the scale of the log probability changes is larger than that in OAI’s TF1 Adam.PyTorch’s Adam presents a more extreme ratio max and min. Here ratio = torch.exp(logprobs_diff). Having a ratio_max=1.8121057748794556 means that for some token, the probability of sampling that token is 1.8x more likely under the current policy, as opposed to only 1.2x with OAI’s TF1 Adam.Larger policy/approxkl policy/clipfrac. Because of the aggressive update, the ratio gets clipped 4.4x more often, and the approximate KL divergence is 6x larger.The aggressive update is likely gonna cause further issues. E.g.,  logprob_diff_mean is 1.7x larger in PyTorch’s Adam, which would correspond to 1.7x larger KL penalty in the next reward calculation; this could get compounded. In fact, this might be related to the famous KL divergence issue — KL penalty is much larger than it should be and the model could pay more attention and optimizes for it more instead, therefore causing negative KL divergence.Larger models get affected more. We conducted experiments comparing PyTorch’s Adam (codename pt_adam) and our custom TensorFlow-style (codename tf_adam) with gpt2 and gpt2-xl. We found that the performance are roughly similar under gpt2; however with gpt2-xl, we observed a more aggressive updates, meaning that larger models get affected by this issue more.When the initial policy updates are more aggressive in gpt2-xl, the training dynamics get affected. For example, we see a much larger objective/kl and objective/scores spikes with pt_adam, especially with sentiment — the biggest KL was as large as 17.5 in one of the random seeds, suggesting an undesirable over-optimization.Furthermore, because of the larger KL, many other training metrics are affected as well. For example, we see a much larger clipfrac (the fraction of time the ratio gets clipped by PPO’s objective clip coefficient 0.2) and approxkl.		Limitations	Noticed this work does not try to reproduce the summarization work in CNN DM or TL;DR. This was because we found the training to be time-consuming and brittle. The particular training run we had showed poor GPU utilization (around 30%), so it takes almost 4 days to perform a training run, which is highly expensive (only AWS sells p3dn.24xlarge, and it costs $31.212 per hour)Additionally, training was brittle. While the reward goes up, we find it difficult to reproduce the “smart copier” behavior reported by Ziegler et al. (2019). Below are some sample outputs — clearly, the agent overfits somehow. See https://wandb.ai/openrlbenchmark/lm-human-preferences/runs/1ab47rqi/logs for more complete logs.		Conclusion	In this work, we took a deep dive into OAI’s original RLHF codebase and compiled a list of its implementation details. We also created a minimal base which reproduces the same learning curves as OAI’s original RLHF codebase, when the dataset and hyperparameters are controlled. Furthermore, we identify surprising implementation details such as the adam optimizer’s setting which causes aggressive updates in early RLHF training. 		Acknowledgement	This work is supported by Hugging Face’s Big Science cluster 🤗. We also thank the helpful discussion with @lewtun and @natolambert.		Bibtex	@article{Huang2023implementation,  author = {Huang, Shengyi and Liu, Tianlin and von Werra, Leandro},  title = {The N Implementation Details of RLHF with PPO},  journal = {Hugging Face Blog},  year = {2023},  note = {https://huggingface.co/blog/the_n_implementation_details_of_rlhf_with_ppo},}