We address the challenge of effective exploration while maintaining good performance in policy gradient methods. As a solution, we propose diverse exploration (DE) via conjugate policies. DE learns and deploys a set of conjugate policies which can be conveniently generated as a byproduct of conjugate gradient descent. We provide both theoretical and empirical results showing the effectiveness of DE at achieving exploration, improving policy performance, and the advantage of DE over exploration by random policy perturbations.
Different generalizations of the policy gradient with the common goal of variance reduction in gradient estimates @cite_20 @cite_16 exist but do not address the same exploration issue studied in this work. An alternate line of work reduces variance using control variates @cite_26 .
@cite_16 @cite_20 @cite_26
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Policy gradient methods have achieved remarkable successes in solving challenging reinforcement learning problems. However, it still often suffers from the large variance issue on policy gradient estimation, which leads to poor sample efficiency during training. In this work, we propose a control variate method to effectively reduce variance for policy gradient methods. Motivated by the Stein's identity, our method extends the previous control variate methods used in REINFORCE and advantage actor-critic by introducing more general action-dependent baseline functions. Empirical studies show that our method significantly improves the sample efficiency of the state-of-the-art policy gradient approaches. Policy gradient methods have achieved remarkable successes in solving challenging reinforcement learning problems. However, it still often suffers from the large variance issue on policy gradient estimation, which leads to poor sample efficiency during training. In this work, we propose a control variate method to effectively reduce variance for policy gradient methods. Motivated by the Stein’s identity, our method extends the previous control variate methods used in REINFORCE and advantage actor-critic by introducing more flexible and general action-dependent baseline functions. Empirical studies show that our method essentially improves the sample efficiency of the state-of-the-art policy gradient approaches. We present and analyze several strategies for improving the performance of stochastic variance-reduced gradient (SVRG) methods. We first show that the convergence rate of these methods can be preserved under a decreasing sequence of errors in the control variate, and use this to derive variants of SVRG that use growing-batch strategies to reduce the number of gradient calculations required in the early iterations. We further (i) show how to exploit support vectors to reduce the number of gradient computations in the later iterations, (ii) prove that the commonly-used regularized SVRG iteration is justified and improves the convergence rate, (iii) consider alternate mini-batch selection strategies, and (iv) consider the generalization error of the method. Policy gradient methods in reinforcement learning have become increasingly prevalent for state-of-the-art performance in continuous control tasks. Novel methods typically benchmark against a few key algorithms such as deep deterministic policy gradients and trust region policy optimization. As such, it is important to present and use consistent baselines experiments. However, this can be difficult due to general variance in the algorithms, hyper-parameter tuning, and environment stochasticity. We investigate and discuss: the significance of hyper-parameters in policy gradients for continuous control, general variance in the algorithms, and reproducibility of reported results. We provide guidelines on reporting novel results as comparisons against baseline methods such that future researchers can make informed decisions when investigating novel methods. Policy gradient methods have been successfully applied to a variety of reinforcement learning tasks. However, while learning in a simulator, these methods do not utilise the opportunity to improve learning by adjusting certain environment variables: unobservable state features that are randomly determined by the environment in a physical setting, but that are controllable in a simulator. This can lead to slow learning, or convergence to highly suboptimal policies. In this paper, we present contextual policy optimisation (CPO). The central idea is to use Bayesian optimisation to actively select the distribution of the environment variable that maximises the improvement generated by each iteration of the policy gradient method. To make this Bayesian optimisation practical, we contribute two easy-to-compute low-dimensional fingerprints of the current policy. We apply CPO to a number of continuous control tasks of varying difficulty and show that CPO can efficiently learn policies that are robust to significant rare events, which are unlikely to be observable under random sampling but are key to learning good policies. Policy gradient is an efficient technique for improving a policy in a reinforcement learning setting. However, vanilla online variants are on-policy only and not able to take advantage of off-policy data. In this paper we describe a new technique that combines policy gradient with off-policy Q-learning, drawing experience from a replay buffer. This is motivated by making a connection between the fixed points of the regularized policy gradient algorithm and the Q-values. This connection allows us to estimate the Q-values from the action preferences of the policy, to which we apply Q-learning updates. We refer to the new technique as 'PGQL', for policy gradient and Q-learning. We also establish an equivalency between action-value fitting techniques and actor-critic algorithms, showing that regularized policy gradient techniques can be interpreted as advantage function learning algorithms. We conclude with some numerical examples that demonstrate improved data efficiency and stability of PGQL. In particular, we tested PGQL on the full suite of Atari games and achieved performance exceeding that of both asynchronous advantage actor-critic (A3C) and Q-learning. In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For each of these criteria, we derive a formula for computing its gradient. We then devise actor-critic algorithms that operate on three timescales--a TD critic on the fastest timescale, a policy gradient (actor) on the intermediate timescale, and a dual ascent for Lagrange multipliers on the slowest timescale. In the discounted setting, we point out the difficulty in estimating the gradient of the variance of the return and incorporate simultaneous perturbation approaches to alleviate this. The average setting, on the other hand, allows for an actor update using compatible features to estimate the gradient of the variance. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in a traffic signal control application. We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates across the action when estimating the gradient, instead of relying only on the action in the sampled trajectory. We establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. We also prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and, for the Gaussian case, with no computational overhead. Finally, we show that it is optimal in a certain sense to explore with a Gaussian policy such that the covariance is proportional to the exponential of the scaled Hessian of the critic with respect to the actions. We present empirical results confirming that this new form of exploration substantially outperforms DPG with the Ornstein-Uhlenbeck heuristic in four challenging MuJoCo domains. Policy gradient methods are widely used for control in reinforcement learning, particularly for the continuous action setting. There have been a host of theoretically sound algorithms proposed for the on-policy setting, due to the existence of the policy gradient theorem which provides a simplified form for the gradient. In off-policy learning, however, where the behaviour policy is not necessarily attempting to learn and follow the optimal policy for the given task, the existence of such a theorem has been elusive. In this work, we solve this open problem by providing the first off-policy policy gradient theorem. The key to the derivation is the use of emphatic weightings. We develop a new actor-critic algorithm---called Actor Critic with Emphatic weightings (ACE)---that approximates the simplified gradients provided by the theorem. We demonstrate in a simple counterexample that previous off-policy policy gradient methods---particularly OffPAC and DPG---converge to the wrong solution whereas ACE finds the optimal solution. Policy search is a successful approach to reinforcement learning. However, policy improvements often result in the loss of information. Hence, it has been marred by premature convergence and implausible solutions. As first suggested in the context of covariant policy gradients (Bagnell and Schneider 2003), many of these problems may be addressed by constraining the information loss. In this paper, we continue this path of reasoning and suggest the Relative Entropy Policy Search (REPS) method. The resulting method differs significantly from previous policy gradient approaches and yields an exact update step. It works well on typical reinforcement learning benchmark problems. Policy gradient algorithms have shown considerable recent success in solving high-dimensional sequential decision making tasks, particularly in robotics. However, these methods often require extensive experience in a domain to achieve high performance. To make agents more sample-efficient, we developed a multi-task policy gradient method to learn decision making tasks consecutively, transferring knowledge between tasks to accelerate learning. Our approach provides robust theoretical guarantees, and we show empirically that it dramatically accelerates learning on a variety of dynamical systems, including an application to quadrotor control. The performance of off-policy learning, including deep Q-learning and deep deterministic policy gradient (DDPG), critically depends on the choice of the exploration policy. Existing exploration methods are mostly based on adding noise to the on-going actor policy and can only explore regions close to what the actor policy dictates. In this work, we develop a simple meta-policy gradient algorithm that allows us to adaptively learn the exploration policy in DDPG. Our algorithm allows us to train flexible exploration behaviors that are independent of the actor policy, yielding a that significantly speeds up the learning process. With an extensive study, we show that our method significantly improves the sample-efficiency of DDPG on a variety of reinforcement learning tasks. Off-policy model-free deep reinforcement learning methods using previously collected data can improve sample efficiency over on-policy policy gradient techniques. On the other hand, on-policy algorithms are often more stable and easier to use. This paper examines, both theoretically and empirically, approaches to merging on- and off-policy updates for deep reinforcement learning. Theoretical results show that off-policy updates with a value function estimator can be interpolated with on-policy policy gradient updates whilst still satisfying performance bounds. Our analysis uses control variate methods to produce a family of policy gradient algorithms, with several recently proposed algorithms being special cases of this family. We then provide an empirical comparison of these techniques with the remaining algorithmic details fixed, and show how different mixing of off-policy gradient estimates with on-policy samples contribute to improvements in empirical performance. The final algorithm provides a generalization and unification of existing deep policy gradient techniques, has theoretical guarantees on the bias introduced by off-policy updates, and improves on the state-of-the-art model-free deep RL methods on a number of OpenAI Gym continuous control benchmarks. Off-policy model-free deep reinforcement learning methods using previously collected data can improve sample efficiency over on-policy policy gradient techniques. On the other hand, on-policy algorithms are often more stable and easier to use. This paper examines, both theoretically and empirically, approaches to merging on- and off-policy updates for deep reinforcement learning. Theoretical results show that off-policy updates with a value function estimator can be interpolated with on-policy policy gradient updates whilst still satisfying performance bounds. Our analysis uses control variate methods to produce a family of policy gradient algorithms, with several recently proposed algorithms being special cases of this family. We then provide an empirical comparison of these techniques with the remaining algorithmic details fixed, and show how different mixing of off-policy gradient estimates with on-policy samples contribute to improvements in empirical performance. The final algorithm provides a generalization and unification of existing deep policy gradient techniques, has theoretical guarantees on the bias introduced by off-policy updates, and improves on the state-of-the-art model-free deep RL methods on a number of OpenAI Gym continuous control benchmarks. We propose a new family of policy gradient methods for reinforcement learning, which alternate between sampling data through interaction with the environment, and optimizing a "surrogate" objective function using stochastic gradient ascent. Whereas standard policy gradient methods perform one gradient update per data sample, we propose a novel objective function that enables multiple epochs of minibatch updates. The new methods, which we call proximal policy optimization (PPO), have some of the benefits of trust region policy optimization (TRPO), but they are much simpler to implement, more general, and have better sample complexity (empirically). Our experiments test PPO on a collection of benchmark tasks, including simulated robotic locomotion and Atari game playing, and we show that PPO outperforms other online policy gradient methods, and overall strikes a favorable balance between sample complexity, simplicity, and wall-time. We consider the fundamental problem in nonconvex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order nonconvex optimization remain to be full gradient descent that converges in O(1 e) iterations for smooth objectives, and stochastic gradient descent that converges in O(1 e2) iterations for objectives that are sum of smooth functions. We provide the first improvement in this line of research. Our result is based on the variance reduction trick recently introduced to convex optimization, as well as a brand new analysis of variance reduction that is suitable for non-convex optimization. For objectives that are sum of smooth functions, our first-order minibatch stochastic method converges with an O(1 e) rate, and is faster than full gradient descent by Ω(n1 3). We demonstrate the effectiveness of our methods on empirical risk minimizations with nonconvex loss functions and training neural nets. We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse solutions both in fully-connected and convolutional layers. This effect is similar to automatic relevance determination effect in empirical Bayes but has a number of advantages. We reduce the number of parameters up to 280 times on LeNet architectures and up to 68 times on VGG-like networks with a negligible decrease of accuracy. We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse solutions both in fully-connected and convolutional layers. This effect is similar to automatic relevance determination effect in empirical Bayes but has a number of advantages. We reduce the number of parameters up to 280 times on LeNet architectures and up to 68 times on VGG-like networks with a negligible decrease of accuracy. In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced variance stochastic gradients. Specifically, the first class called the nonconvex stochastic variance reduced gradient ADMM (SVRG-ADMM), uses a multi-stage scheme to progressively reduce the variance of stochastic gradients. The second is the nonconvex stochastic average gradient ADMM (SAG-ADMM), which additionally uses the old gradients estimated in the previous iteration. The third called SAGA-ADMM is an extension of the SAG-ADMM method. Moreover, under some mild conditions, we establish the iteration complexity bound of @math of the proposed methods to obtain an @math -stationary solution of the nonconvex optimizations. In particular, we provide a general framework to analyze the iteration complexity of these nonconvex stochastic ADMM methods with variance reduction. Finally, some numerical experiments demonstrate the effectiveness of our methods. Policy gradient reinforcement learning has been applied to two-player alternate-turn zero-sum games, e.g., in AlphaGo, self-play REINFORCE was used to improve the neural net model after supervised learning. In this paper, we emphasize that two-player zero-sum games with alternating turns, which have been previously formulated as Alternating Markov Games (AMGs), are different from standard MDP because of their two-agent nature. We exploit the difference in associated Bellman equations, which leads to different policy iteration algorithms. As policy gradient method is a kind of generalized policy iteration, we show how these differences in policy iteration are reflected in policy gradient for AMGs. We formulate an adversarial policy gradient and discuss potential possibilities for developing better policy gradient methods other than self-play REINFORCE. The core idea is to estimate the minimum rather than the mean for the “critic”. Experimental results on the game of Hex show the modified Monte Carlo policy gradient methods are able to learn better pure neural net policies than the REINFORCE variants. To apply learned neural weights to multiple board sizes Hex, we describe a board-size independent neural net architecture. We show that when combined with search, using a single neural net model, the resulting program consistently beats MoHex 2.0, the state-of-the-art computer Hex player, on board sizes from 9×9 to 13×13.