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Model-free reinforcement learning algorithms combined with value function approximation have recently achieved impressive performance in a variety of application domains. However, the theoretical understanding of such algorithms is limited, and existing results are largely focused on episodic or discounted Markov decision processes (MDPs). In this work, we present adaptive approximate policy iteration (AAPI), a learning scheme which enjoys a $tilde{O}(T^{2/3})$ regret bound for undiscounted, continuing learning in uniformly ergodic MDPs. This is an improvement over the best existing bound of $tilde{O}(T^{3/4})$ for the average-reward case with function approximation. Our algorithm and analysis rely on online learning techniques, where value functions are treated as losses. The main technical novelty is the use of a data-dependent adaptive learning rate coupled with a so-called optimistic prediction of upcoming losses. In addition to theoretical guarantees, we demonstrate the advantages of our approach empirically on several environments.
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Off-policy evaluation provides an essential tool for evaluating the effects of different policies or treatments using only observed data. When applied to high-stakes scenarios such as medical diagnosis or financial decision-making, it is crucial to provide provably correct upper and lower bounds of the expected reward, not just a classical single point estimate, to the end-users, as executing a poor policy can be very costly. In this work, we propose a provably correct method for obtaining interval bounds for off-policy evaluation in a general continuous setting. The idea is to search for the maximum and minimum values of the expected reward among all the Lipschitz Q-functions that are consistent with the observations, which amounts to solving a constrained optimization problem on a Lipschitz function space. We go on to introduce a Lipschitz value iteration method to monotonically tighten the interval, which is simple yet efficient and provably convergent. We demonstrate the practical efficiency of our method on a range of benchmarks.
In this work, we study algorithms for learning in infinite-horizon undiscounted Markov decision processes (MDPs) with function approximation. We first show that the regret analysis of the Politex algorithm (a version of regularized policy iteration) can be sharpened from $O(T^{3/4})$ to $O(sqrt{T})$ under nearly identical assumptions, and instantiate the bound with linear function approximation. Our result provides the first high-probability $O(sqrt{T})$ regret bound for a computationally efficient algorithm in this setting. The exact implementation of Politex with neural network function approximation is inefficient in terms of memory and computation. Since our analysis suggests that we need to approximate the average of the action-value functions of past policies well, we propose a simple efficient implementation where we train a single Q-function on a replay buffer with past data. We show that this often leads to superior performance over other implementation choices, especially in terms of wall-clock time. Our work also provides a novel theoretical justification for using experience replay within policy iteration algorithms.
For artificially intelligent learning systems to have widespread applicability in real-world settings, it is important that they be able to operate decentrally. Unfortunately, decentralized control is difficult -- computing even an epsilon-optimal joint policy is a NEXP complete problem. Nevertheless, a recently rediscovered insight -- that a team of agents can coordinate via common knowledge -- has given rise to algorithms capable of finding optimal joint policies in small common-payoff games. The Bayesian action decoder (BAD) leverages this insight and deep reinforcement learning to scale to games as large as two-player Hanabi. However, the approximations it uses to do so prevent it from discovering optimal joint policies even in games small enough to brute force optimal solutions. This work proposes CAPI, a novel algorithm which, like BAD, combines common knowledge with deep reinforcement learning. However, unlike BAD, CAPI prioritizes the propensity to discover optimal joint policies over scalability. While this choice precludes CAPI from scaling to games as large as Hanabi, empirical results demonstrate that, on the games to which CAPI does scale, it is capable of discovering optimal joint policies even when other modern multi-agent reinforcement learning algorithms are unable to do so. Code is available at https://github.com/ssokota/capi .
Controlling the movements of highly articulated agents and robots has been a long-standing challenge to model-free deep reinforcement learning. In this paper, we propose a simple, yet general, framework for improving the performance of policy gradient algorithms by discretizing the continuous action space. Instead of using a fixed set of predetermined atomic actions, we exploit particle filtering to adaptively discretize actions during training and track the posterior policy distribution represented as a mixture of Gaussians. The resulting policy can replace the original continuous policy of any given policy gradient algorithm without changing its underlying model architecture. We demonstrate the applicability of our approach to state-of-the-art on-policy and off-policy baselines in challenging control tasks. Baselines using our particle-based policies achieve better final performance and speed of convergence as compared to corresponding continuous implementations and implementations that rely on fixed discretization schemes.
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