Symbolic method for deriving policy in reinforcement learning

This paper addresses the problem of deriving a policy from the value function in the context of reinforcement learning in continuous state and input spaces. We propose a novel method based on genetic programming to construct a symbolic function, which serves as a proxy to the value function and from which a continuous policy is derived. The symbolic proxy function is constructed such that it maximizes the number of correct choices of the control input for a set of selected states. Maximization methods can then be used to derive a control policy that performs better than the policy derived from the original approximate value function. The method was experimentally evaluated on two control problems with continuous spaces, pendulum swing-up and magnetic manipulation, and compared to a standard policy derivation method using the value function approximation. The results show that the proposed method and its variants outperform the standard method.Accepted Author ManuscriptOLD Intelligent Control & Robotic

Proxy functions for Approximate Reinforcement Learning

Approximate Reinforcement Learning (RL) is a method to solve sequential decisionmaking and dynamic control problems in an optimal way. This paper addresses RL for continuous state spaces which derive the control policy by using an approximate value function (V-function). The standard approach to derive a policy through the V-function is analogous to hill climbing: at each state the RL agent chooses the control input that maximizes the right-hand side of the Bellman equation. Although theoretically optimal, the actual control performance of this method is heavily influenced by the local smoothness of the V-function; a lack of smoothness results in undesired closed-loop behavior with input chattering or limit-cycles. To circumvent these problems, this paper provides a method based on Symbolic Regression to generate a locally smooth proxy to the V-function. The proposed method has been evaluated on two nonlinear control benchmarks: pendulum swing-up and magnetic manipulation. The new method has been compared with the standard policy derivation technique using the approximate V-function and the results show that the proposed approach outperforms the standard one with respect to the cumulative return.Learning & Autonomous Contro

Policy derivation methods for critic-only reinforcement learning in continuous spaces

This paper addresses the problem of deriving a policy from the value function in the context of critic-only reinforcement learning (RL) in continuous state and action spaces. With continuous-valued states, RL algorithms have to rely on a numerical approximator to represent the value function. Numerical approximation due to its nature virtually always exhibits artifacts which damage the overall performance of the controlled system. In addition, when continuous-valued action is used, the most common approach is to discretize the action space and exhaustively search for the action that maximizes the right-hand side of the Bellman equation. Such a policy derivation procedure is computationally involved and results in steady-state error due to the lack of continuity. In this work, we propose policy derivation methods which alleviate the above problems by means of action space refinement, continuous approximation, and post-processing of the V-function by using symbolic regression. The proposed methods are tested on nonlinear control problems: 1-DOF and 2-DOF pendulum swing-up problems, and on magnetic manipulation. The results show significantly improved performance in terms of cumulative return and computational complexity.Accepted Author ManuscriptLearning & Autonomous Contro

Optimal control via reinforcement learning with symbolic policy approximation

Model-based reinforcement learning (RL) algorithms can be used to derive optimal control laws for nonlinear dynamic systems. With continuous-valued state and input variables, RL algorithms have to rely on function approximators to represent the value function and policy mappings. This paper addresses the problem of finding a smooth policy based on the value function represented by means of a basis-function approximator. We first show that policies derived directly from the value function or represented explicitly by the same type of approximator lead to inferior control performance, manifested by non-smooth control signals and steady-state errors. We then propose a novel method to construct a smooth policy represented by an analytic equation, obtained by means of symbolic regression. The proposed method is illustrated on a reference-tracking problem of a 1-DOF robot arm operating under the influence of gravity. The results show that the analytic control law performs at least equally well as the original numerically approximated policy, while it leads to much smoother control signals. In addition, the analytic function is readable (as opposed to black-box approximators) and can be used in further analysis and synthesis of the closed loop.Learning & Autonomous Contro