We consider continuous state, continuous action batch reinforcement learning where the goal is to learn a good policy from a sufficiently rich trajectory generated by another policy. We study a variant of fitted Q-iteration, where the greedy action selection is replaced by searching for a policy in a restricted set of candidate policies by maximizing the average action values. We provide a rigorous theoretical analysis of this algorithm, proving what we believe is the first finite-time bounds for value-function based algorithms for continuous state- and action-space problems.

We study the problem of an apprentice learning to behave in an environment with an unknown reward function by observing the behavior of an expert. We follow on the work of Abbeel and Ng [1] who considered a framework in which the true reward function is assumed to be a linear combination of a set of known and observable features. We give a new algorithm that, like theirs, is guaranteed to learn a policy that is nearly as good as the expert's, given enough examples. However, unlike their algorithm, we show that ours may produce a policy that is substantially better than the expert's. Moreover, our algorithm is computationally faster, is easier to implement, and can be applied even in the absence of an expert.

Electrical power management in large-scale IT systems such as commercial data- centers is an application area of rapidly growing interest from both an economic and ecological perspective, with billions of dollars and millions of metric tons of CO2 emissions at stake annually. Businesses want to save power without sac- rificing performance. This paper presents a reinforcement learning approach to simultaneous online management of both performance and power consumption. We apply RL in a realistic laboratory testbed using a Blade cluster and dynam- ically varying HTTP workload running on a commercial web applications mid- dleware platform. We embed a CPU frequency controller in the Blade servers' firmware, and we train policies for this controller using a multi-criteria reward signal depending on both application performance and CPU power consumption.

We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic rein- forcement learning methods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their com- patibility with function approximation methods, which are needed to handle large or in(cid:2)nite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further re- duce variance in some cases.

We consider apprenticeship learning--learning from expert demonstrations--in the setting of large, complex domains. Past work in apprenticeship learning requires that the expert demonstrate complete trajectories through the domain. However, in many problems even an expert has difficulty controlling the system, which makes this approach infeasible. For example, consider the task of teach- ing a quadruped robot to navigate over extreme terrain; demonstrating an optimal policy (i.e., an optimal set of foot locations over the entire terrain) is a highly non-trivial task, even for an expert. In this paper we propose a method for hier- archical apprenticeship learning, which allows the algorithm to accept isolated advice at different hierarchical levels of the control task.

We derive an equation for temporal difference learning from statistical principles. Specifically, we start with the variational principle and then bootstrap to produce an updating rule for discounted state value estimates. The resulting equation is similar to the standard equation for temporal difference learning with eligibil- ity traces, so called TD(λ), however it lacks the parameter α that specifies the learning rate. In the place of this free parameter there is now an equation for the learning rate that is specific to each state transition. We experimentally test this new learning rule against TD(λ) and find that it offers superior performance in various settings.

Learning in real-world domains often requires to deal with continuous state and action spaces. Although many solutions have been proposed to apply Reinforce- ment Learning algorithms to continuous state problems, the same techniques can be hardly extended to continuous action spaces, where, besides the computation of a good approximation of the value function, a fast method for the identification of the highest-valued action is needed. In this paper, we propose a novel actor-critic approach in which the policy of the actor is estimated through sequential Monte Carlo methods. The importance sampling step is performed on the basis of the values learned by the critic, while the resampling step modifies the actor's policy. The proposed approach has been empirically compared to other learning algo- rithms into several domains; in this paper, we report results obtained in a control problem consisting of steering a boat across a river.

Actor-critic algorithms for reinforcement learning are achieving renewed popularity due to their good convergence properties in situations where other approaches often fail (e.g., when function approximation is involved). Interestingly, there is growing evidence that actor-critic approaches based on phasic dopamine signals play a key role in biological learning through the cortical and basal ganglia. We derive a temporal difference based actor critic learning algorithm, for which convergence can be proved without assuming separate time scales for the actor and the critic. The approach is demonstrated by applying it to networks of spiking neurons. The established relation between phasic dopamine and the temporal difference signal lends support to the biological relevance of such algorithms.

The essence of exploration is acting to try to decrease uncertainty. We propose a new methodology for representing uncertainty in continuous-state control problems. Our approach, multi-resolution exploration (MRE), uses a hierarchical mapping to identify regions of the state space that would benefit from additional samples. We demonstrate MRE's broad utility by using it to speed up learning in a prototypical model-based and value-based reinforcement-learning method. Empirical results show that MRE improves upon state-of-the-art exploration approaches.

We use graphical models and structure learning to explore how people learn policies in sequential decision making tasks. Studies of sequential decision-making in humans frequently find suboptimal performance relative to an ideal actor that knows the graph model that generates reward in the environment. We argue that the learning problem humans face also involves learning the graph structure for reward generation in the environment. We formulate the structure learning problem using mixtures of reward models, and solve the optimal action selection problem using Bayesian Reinforcement Learning. We show that structure learning in one and two armed bandit problems produces many of the qualitative behaviors deemed suboptimal in previous studies.