Q-learning can be difficult to use in continuous action spaces, because an optimization has to be solved to find the maximal action for the action-values. A common strategy has been to restrict the functional form of the action-values to be concave in the actions, to simplify the optimization. Such restrictions, however, can prevent learning accurate action-values. In this work, we propose a new policy search objective that facilitates using Q-learning and a framework to optimize this objective, called Actor-Expert. The Expert uses Qlearning to update the action-values towards optimal action-values. The Actor learns the maximal actions over time for these changing action-values. We develop a Cross Entropy Method (CEM) for the Actor, where such a global optimization approach facilitates use of generically parameterized action-values. This method-which we call Conditional CEMiteratively concentrates density around maximal actions, conditioned on state. We prove that this algorithm tracks the expected CEM update, over states with changing actionvalues. We demonstrate in a toy environment that previous methods that restrict the action-value parameterization fail whereas Actor-Expert with a more general action-value parameterization succeeds. Finally, we demonstrate that Actor-Expert performs as well as or better than competitors on four benchmark continuous-action environments.

In this paper, we provide two new stable online algorithms for the problem of prediction in reinforcement learning, i.e., estimating the value function of a model-free Markov reward process using the linear function approximation architecture and with memory and computation costs scaling quadratically in the size of the feature set. The algorithms employ the multi-timescale stochastic approximation variant of the very popular cross entropy optimization method which is a model based search method to find the global optimum of a real-valued function. A proof of convergence of the algorithms using the ODE method is provided. We supplement our theoretical results with experimental comparisons. The algorithms achieve good performance fairly consistently on many RL benchmark problems with regards to computational efficiency, accuracy and stability.

In this paper, we consider a modified version of the control problem in a model free Markov decision process (MDP) setting with large state and action spaces. The control problem most commonly addressed in the contemporary literature is to find an optimal policy which maximizes the value function, i.e., the long run discounted reward of the MDP. The current settings also assume access to a generative model of the MDP with the hidden premise that observations of the system behaviour in the form of sample trajectories can be obtained with ease from the model. In this paper, we consider a modified version, where the cost function is the expectation of a non-convex function of the value function without access to the generative model. Rather, we assume that a sample trajectory generated using a priori chosen behaviour policy is made available. In this restricted setting, we solve the modified control problem in its true sense, i.e., to find the best possible policy given this limited information. We propose a stochastic approximation algorithm based on the wellknown cross entropy method which is data (sample trajectory) efficient, stable, robust as well as computationally and storage efficient. We provide a proof of convergence of our algorithm to a policy which is globally optimal relative to the behaviour policy. We also present experimental results to corroborate our claims and we demonstrate the superiority of the solution produced by our algorithm compared to the state-of-the-art algorithms under appropriately chosen behaviour policy.

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