Counterfactual Regret Minimization (CFR) is the most successful algorithm for finding approximate Nash equilibria in imperfect information games. However, CFR's reliance on full game-tree traversals limits its scalability. For this reason, the game's state- and action-space is often abstracted (i.e. simplified) for CFR, and the resulting strategy is then translated back to the full game, which requires extensive expert-knowledge and often converges to highly exploitable policies. A recently proposed method, Deep CFR, applies deep learning directly to CFR, allowing the agent to intrinsically abstract and generalize over the state-space from samples, without requiring expert knowledge. In this paper, we introduce Single Deep CFR (SD-CFR), a simplified variant of Deep CFR that has a lower overall approximation error by avoiding the training of an average strategy network. We show that SD-CFR is more attractive from a theoretical perspective and empirically outperforms Deep CFR with respect to exploitability and one-on-one play in poker.
To the best of our knowledge, @cite_30 was the first algorithm to soundly apply deep reinforcement learning (deep RL) from single trajectory samples to large extensive-form games. While not showing record-breaking results in terms of exploitability, NFSP was able to learn a competitive strategy in Limit Texas Hold'em Poker over just 14 GPU days.
@cite_30
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Deep reinforcement learning (RL) has achieved many recent successes, yet experiment turn-around time remains a key bottleneck in research and in practice. We investigate how to optimize existing deep RL algorithms for modern computers, specifically for a combination of CPUs and GPUs. We confirm that both policy gradient and Q-value learning algorithms can be adapted to learn using many parallel simulator instances. We further find it possible to train using batch sizes considerably larger than are standard, without negatively affecting sample complexity or final performance. We leverage these facts to build a unified framework for parallelization that dramatically hastens experiments in both classes of algorithm. All neural network computations use GPUs, accelerating both data collection and training. Our results include using an entire NVIDIA DGX-1 to learn successful strategies in Atari games in single-digit minutes, using both synchronous and asynchronous algorithms. Many real-world applications can be described as large-scale games of imperfect information. To deal with these challenging domains, prior work has focused on computing Nash equilibria in a handcrafted abstraction of the domain. In this paper we introduce the first scalable end-to-end approach to learning approximate Nash equilibria without prior domain knowledge. Our method combines fictitious self-play with deep reinforcement learning. When applied to Leduc poker, Neural Fictitious Self-Play (NFSP) approached a Nash equilibrium, whereas common reinforcement learning methods diverged. In Limit Texas Holdem, a poker game of real-world scale, NFSP learnt a strategy that approached the performance of state-of-the-art, superhuman algorithms based on significant domain expertise. Despite significant advances in the field of deep Reinforcement Learning (RL), today's algorithms still fail to learn human-level policies consistently over a set of diverse tasks such as Atari 2600 games. We identify three key challenges that any algorithm needs to master in order to perform well on all games: processing diverse reward distributions, reasoning over long time horizons, and exploring efficiently. In this paper, we propose an algorithm that addresses each of these challenges and is able to learn human-level policies on nearly all Atari games. A new transformed Bellman operator allows our algorithm to process rewards of varying densities and scales; an auxiliary temporal consistency loss allows us to train stably using a discount factor of @math (instead of @math ) extending the effective planning horizon by an order of magnitude; and we ease the exploration problem by using human demonstrations that guide the agent towards rewarding states. When tested on a set of 42 Atari games, our algorithm exceeds the performance of an average human on 40 games using a common set of hyper parameters. Furthermore, it is the first deep RL algorithm to solve the first level of Montezuma's Revenge. Deep reinforcement learning (RL) has achieved several high profile successes in difficult decision-making problems. However, these algorithms typically require a huge amount of data before they reach reasonable performance. In fact, their performance during learning can be extremely poor. This may be acceptable for a simulator, but it severely limits the applicability of deep RL to many real-world tasks, where the agent must learn in the real environment. In this paper we study a setting where the agent may access data from previous control of the system. We present an algorithm, Deep Q-learning from Demonstrations (DQfD), that leverages small sets of demonstration data to massively accelerate the learning process even from relatively small amounts of demonstration data and is able to automatically assess the necessary ratio of demonstration data while learning thanks to a prioritized replay mechanism. DQfD works by combining temporal difference updates with supervised classification of the demonstrator's actions. We show that DQfD has better initial performance than Prioritized Dueling Double Deep Q-Networks (PDD DQN) as it starts with better scores on the first million steps on 41 of 42 games and on average it takes PDD DQN 83 million steps to catch up to DQfD's performance. DQfD learns to out-perform the best demonstration given in 14 of 42 games. In addition, DQfD leverages human demonstrations to achieve state-of-the-art results for 11 games. Finally, we show that DQfD performs better than three related algorithms for incorporating demonstration data into DQN.