Exploration strategy design is one of the challenging problems in reinforcement learning (RL), especially when the environment contains a large state space or sparse rewards. During exploration, the agent tries to discover novel areas or high reward (quality) areas. In most existing methods, the novelty and quality in the neighboring area of the current state are not well utilized to guide the exploration of the agent. To tackle this problem, we propose a novel RL framework, called c lustered r einforcement l earning (CRL), for efficient exploration in RL. CRL adopts clustering to divide the collected states into several clusters, based on which a bonus reward reflecting both novelty and quality in the neighboring area (cluster) of the current state is given to the agent. Experiments on a continuous control task and several games show that CRL can outperform other state-of-the-art methods to achieve the best performance in most cases.
In finite MDPs, @math @cite_12 , R-Max @cite_28 and UCRL @cite_11 all make use of state-action counts and are activated by the idea of optimism under uncertainty. @math @cite_12 determines online to choose an efficient learning policy. R-Max @cite_28 assumes the received reward is not in quality area and trains a fictitious model to learn the optimal policy. UCRL @cite_11 chooses an optimistic policy by using upper confidence bounds. Bayesian RL methods maintain a distribution of belief state as the uncertainty over possible MDPs @cite_25 @cite_19 @cite_13 @cite_3 and use counts to explore .
@cite_28 @cite_3 @cite_19 @cite_13 @cite_25 @cite_12 @cite_11
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We consider the problem of provably optimal exploration in reinforcement learning for finite horizon MDPs. We show that an optimistic modification to value iteration achieves a regret bound of @math where @math is the time horizon, @math the number of states, @math the number of actions and @math the number of time-steps. This result improves over the best previous known bound @math achieved by the UCRL2 algorithm of , 2010. The key significance of our new results is that when @math and @math , it leads to a regret of @math that matches the established lower bound of @math up to a logarithmic factor. Our analysis contains two key insights. We use careful application of concentration inequalities to the optimal value function as a whole, rather than to the transitions probabilities (to improve scaling in @math ), and we define Bernstein-based "exploration bonuses" that use the empirical variance of the estimated values at the next states (to improve scaling in @math ). We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria. The first stopping criterion controls the growth rate of episode length. The second stopping criterion happens when the number of visits to any state-action pair is doubled. We establish @math bounds on expected regret under a Bayesian setting, where @math and @math are the sizes of the state and action spaces, @math is time, and @math is the bound of the span. This regret bound matches the best available bound for weakly communicating MDPs. Numerical results show it to perform better than existing algorithms for infinite horizon MDPs. We consider the problem of power allocation over one or more time-varying channels with unknown distributions in energy harvesting communications. In the single-channel case, the transmitter chooses the transmit power based on the amount of stored energy in its battery with the goal of maximizing the average rate over time. We model this problem as a Markov decision process (MDP) with transmitter as the agent, battery status as the state, transmits power as the action and rate as the reward. The average reward maximization problem can be modeled by a linear program (LP) that uses the transition probabilities for the state-action pairs and their reward values to select a power allocation policy. This problem is challenging because the uncertainty in channels implies that the mean rewards associated with the state-action pairs are unknown. We therefore propose two online learning algorithms: linear program of sample means (LPSM) and Epoch-LPSM that learn these rewards and adapt their policies over time. For both algorithms, we prove that their regret is upper-bounded by a constant. To our knowledge this is the first result showing constant regret learning algorithms for MDPs with unknown mean rewards. We also prove an even stronger result about LPSM: that its policy matches the optimal policy exactly in finite expected time. Epoch-LPSM incurs a higher regret compared with the LPSM, while reducing the computational requirements substantially. We further consider a multi-channel scenario, where the agent also chooses a channel in each slot, and present our multi-channel LPSM (MC-LPSM) algorithm that explores different channels and uses that information to solve the LP during exploitation. MC-LPSM incurs a regret that scales logarithmically in time and linearly in the number of channels. Through a matching lower bound on the regret of any algorithm, we also prove the asymptotic order optimality of MC-LPSM. Consider the problem of approximating the optimal policy of a Markov decision process (MDP) by sampling state transitions. In contrast to existing reinforcement learning methods that are based on successive approximations to the nonlinear Bellman equation, we propose a Primal-Dual @math Learning method in light of the linear duality between the value and policy. The @math learning method is model-free and makes primal-dual updates to the policy and value vectors as new data are revealed. For infinite-horizon undiscounted Markov decision process with finite state space @math and finite action space @math , the @math learning method finds an @math -optimal policy using the following number of sample transitions @math where @math is an upper bound of mixing times across all policies and @math is a parameter characterizing the range of stationary distributions across policies. The @math learning method also applies to the computational problem of MDP where the transition probabilities and rewards are explicitly given as the input. In the case where each state transition can be sampled in @math time, the @math learning method gives a sublinear-time algorithm for solving the averaged-reward MDP.