Solving Factored MDPs with Hybrid State and Action Variables

Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a new hybrid approximate linear programming (HALP) framework that permits their efficient solutions. The central idea of HALP is to approximate the optimal value function by a linear combination of basis functions and optimize its weights by linear programming. We analyze both theoretical and computational aspects of this approach, and demonstrate its scale-up potential on several hybrid optimization problems

Planning in Hybrid Structured Stochastic Domains

Efficient representations and solutions for large structured decision problems with continuous and discrete variables are among the important challenges faced by the designers of automated decision support systems. In this work, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a hybrid approximate linear programming (HALP) framework that permits their efficient solutions. The central idea of HALP is to approximate the optimal value function of an MDP by a linear combination of basis functions and optimize its weights by linear programming. We study both theoretical and practical aspects of this approach, and demonstrate its scale-up potential on several hybrid optimization problems

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

Reinforcement Learning with Parameterized Actions

We introduce a model-free algorithm for learning in Markov decision processes with parameterized actions-discrete actions with continuous parameters. At each step the agent must select both which action to use and which parameters to use with that action. We introduce the Q-PAMDP algorithm for learning in these domains, show that it converges to a local optimum, and compare it to direct policy search in the goal-scoring and Platform domains.Comment: Accepted for AAAI 201

Factored temporal difference learning in the new ties environment

Although reinforcement learning is a popular method for training an agent for decision making based on rewards, well studied tabular methods are not applicable for large, realistic problems. In this paper, we experiment with a factored version of temporal difference learning, which boils down to a linear function approximation scheme utilising natural features coming from the structure of the task. We conducted experiments in the New Ties environment, which is a novel platform for multi-agent simulations. We show that learning utilising a factored representation is effective even in large state spaces, furthermore it outperforms tabular methods even in smaller problems both in learning speed and stability, because of its generalisation capabilities

Factored Value Iteration Converges

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we uniformly sample polynomially many samples from the (exponentially large) state space. This way, the complexity of our algorithm becomes polynomial in the size of the fMDP description length. We prove that the algorithm is convergent. We also derive an upper bound on the difference between our approximate solution and the optimal one, and also on the error introduced by sampling. We analyze various projection operators with respect to their computation complexity and their convergence when combined with approximate value iteration.Comment: 17 pages, 1 figur