We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of uncertainty. Beside the existence of an optimal policy which satisfies the Poisson equation, the only assumptions made are Hölder continuity of rewards and transition probabilities.

We propose Deterministic Sequencing of Exploration and Exploitation (DSEE) algorithm with interleaving exploration and exploitation epochs for model-based RL problems that aim to simultaneously learn the system model, i.e., a Markov decision process (MDP), and the associated optimal policy. During exploration, DSEE explores the environment and updates the estimates for expected reward and transition probabilities. During exploitation, the latest estimates of the expected reward and transition probabilities are used to obtain a robust policy with high probability. We design the lengths of the exploration and exploitation epochs such that the cumulative regret grows as a sub-linear function of time.

For this For reinforcement learning in MDP with changes in reward problem setting, we propose an algorithm and function and transition probabilities, we provide provide performance guarantees for the regret an algorithm, UCRL with Restarts, a version of UCRL evaluated against the optimal non-stationary [Jaksch et al., 2010], which restarts according to a schedule policy. The upper bound on the regret is given dependent on the variation in the MDP (defined in terms of the total variation in the MDP. in Section 2 below). We derive a high-probability upper This is the first variational regret bound for the bound on the cumulative regret of our algorithm of general reinforcement learning setting.

This paper presents a reinforcement learning algorithm for solving infinite horizon Markov Decision Processes under the expected total discounted reward criterion when both the state and action spaces are continuous. This algorithm is based on Watkins' Q-learning, but uses Nadaraya-Watson kernel smoothing to generalize knowledge to unvisited states. As expected, continuity conditions must be imposed on the mean rewards and transition probabilities. Using results from kernel regression theory, this algorithm is proven capable of producing a Q-value function estimate that is uniformly within an arbitrary tolerance of the true Q-value function with probability one. The algorithm is then applied to an example problem to empirically show convergence as well.

We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of uncertainty. Beside the existence of an optimal policy which satisfies the Poisson equation, the only assumptions made are Hoelder continuity of rewards and transition probabilities.

We consider the restless Markov bandit problem, in which the state of each arm evolves according to a Markov process independently of the learner's actions. We suggest an algorithm that after $T$ steps achieves $\tilde{O}(\sqrt{T})$ regret with respect to the best policy that knows the distributions of all arms. No assumptions on the Markov chains are made except that they are irreducible. In addition, we show that index-based policies are necessarily suboptimal for the considered problem.