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We consider a team of reinforcement learning agents that concurrently operate in a common environment, and we develop an approach to efficient coordinated exploration that is suitable for problems of practical scale. Our approach builds on seed sampling[1] and randomized value function learning [11]. We demonstrate that, for simple tabular contexts, the approach is competitive with previously proposed tabular model learning methods [1]. With a higher-dimensional problem and a neural network value function representation, the approach learns quickly with far fewer agents than alternative exploration schemes.

We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments, including linear bandits, tabular MDPs, and factored MDPs. These examples demonstrate the potential of a general information-theoretic approach for the design and analysis of reinforcement learning algorithms.

We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments, including linear bandits, tabular MDPs, and factored MDPs. These examples demonstrate the potential of a general information-theoretic approach for the design and analysis of reinforcement learning algorithms.

E cient exploration remains a major challenge for reinforcement learning (RL). Common dithering strategies for exploration, such as '-greedy, do not carry out temporally-extended (or deep) exploration; this can lead to exponentially larger data requirements. However, most algorithms for statistically e cient RL are not computationally tractable in complex environments. Randomized value functions o er a promising approach to e cient exploration with generalization, but existing algorithms are not compatible with nonlinearly parameterized value functions. As a first step towards addressing such contexts we develop bootstrapped DQN. We demonstrate that bootstrapped DQN can combine deep exploration with deep neural networks for exponentially faster learning than any dithering strategy. In the Arcade Learning Environment bootstrapped DQN substantially improves learning speed and cumulative performance across most games.

However, this dependence is through entropy, which can become arbitrarily large as the number of actions increases. We establish new bounds that depend instead on a notion of rate-distortion. Among other things, this allows us to recover through information-theoretic arguments a near-optimal bound for the linear bandit. We also offer a bound for the logistic bandit that dramatically improves on the best previously available, though this bound depends on an information-theoretic statistic that we have only been able to quantify via computation.

Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e., guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in contextual linear bandits that have application in many different fields including personalized recommendation. We formulate a notion of safety for this class of algorithms. We develop a safe contextual linear bandit algorithm, called conservative linear UCB (CLUCB), that simultaneously minimizes its regret and satisfies the safety constraint, i.e., maintains its performance above a fixed percentage of the performance of a baseline strategy, uniformly over time. We prove an upper-bound on the regret of CLUCB and show that it can be decomposed into two terms: 1) an upper-bound for the regret of the standard linear UCB algorithm that grows with the time horizon and 2) a constant term that accounts for the loss of being conservative in order to satisfy the safety constraint. We empirically show that our algorithm is safe and validate our theoretical analysis.

Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for simple special cases. This paper develops ensemble sampling, which aims to approximate Thompson sampling while maintaining tractability even in the face of complex models such as neural networks. Ensemble sampling dramatically expands on the range of applications for which Thompson sampling is viable. We establish a theoretical basis that supports the approach and present computational results that offer further insight.

We consider a team of reinforcement learning agents that concurrently operate in a common environment, and we develop an approach to efficient coordinated exploration that is suitable for problems of practical scale. Our approach builds on seed sampling[1] and randomized value function learning [11]. We demonstrate that, for simple tabular contexts, the approach is competitive with previously proposed tabular model learning methods [1]. With a higher-dimensional problem and a neural network value function representation, the approach learns quickly with far fewer agents than alternative exploration schemes.

Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for simple special cases. This paper develops ensemble sampling, which aims to approximate Thompson sampling while maintaining tractability even in the face of complex models such as neural networks. Ensemble sampling dramatically expands on the range of applications for which Thompson sampling is viable. We establish a theoretical basis that supports the approach and present computational results that offer further insight.