Pseudorehearsal in value function approximation

Catastrophic forgetting is of special importance in reinforcement learning, as the data distribution is generally non-stationary over time. We study and compare several pseudorehearsal approaches for Q-learning with function approximation in a pole balancing task. We have found that pseudorehearsal seems to assist learning even in such very simple problems, given proper initialization of the rehearsal parameters

Weak approximation over function fields

We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.Comment: 22 page

Global Optimization for Value Function Approximation

Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation, which employs global optimization. The formulation provides strong a priori guarantees on both robust and expected policy loss by minimizing specific norms of the Bellman residual. Solving a bilinear program optimally is NP-hard, but this is unavoidable because the Bellman-residual minimization itself is NP-hard. We describe and analyze both optimal and approximate algorithms for solving bilinear programs. The analysis shows that this algorithm offers a convergent generalization of approximate policy iteration. We also briefly analyze the behavior of bilinear programming algorithms under incomplete samples. Finally, we demonstrate that the proposed approach can consistently minimize the Bellman residual on simple benchmark problems

Loop Calculus for Non-Binary Alphabets using Concepts from Information Geometry

The Bethe approximation is a well-known approximation of the partition function used in statistical physics. Recently, an equality relating the partition function and its Bethe approximation was obtained for graphical models with binary variables by Chertkov and Chernyak. In this equality, the multiplicative error in the Bethe approximation is represented as a weighted sum over all generalized loops in the graphical model. In this paper, the equality is generalized to graphical models with non-binary alphabet using concepts from information geometry.Comment: 18 pages, 4 figures, submitted to IEEE Trans. Inf. Theor