In many robotic applications, some aspects of the system dynamics can be modeled accurately while others are difficult to obtain or model. We present a novel reinforcement learning (RL) method for continuous state and action spaces that learns with partial knowledge of the system and without active exploration. It solves linearly-solvable Markov decision processes (L-MDPs), which are well suited for continuous state and action spaces, based on an actor-critic architecture. Compared to previous RL methods for L-MDPs and path integral methods which are model based, the actor-critic learning does not need a model of the uncontrolled dynamics and, importantly, transition noise levels; however, it requires knowing the control dynamics for the problem. We evaluate our method on two synthetic test problems, and one real-world problem in simulation and using real traffic data. Our experiments demonstrate improved learning and policy performance.
Previous approaches for solving L-MDPs are predominantly model based @cite_13 @cite_15 @cite_16 . These efficiently optimize control policies by solving the linearized Bellman in discrete- or continuous-state L-MDPs when the system dynamics is fully known. Our method relaxes this requirement using samples of passive dynamics, while knowing the control dynamics. We also introduce multi-layer neural networks for approximating the value functions in L-MDPs in addition to the previously used radial basis functions.
@cite_15 @cite_16 @cite_13
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We introduce a class of MPDs which greatly simplify Reinforcement Learning. They have discrete state spaces and continuous control spaces. The controls have the effect of rescaling the transition probabilities of an underlying Markov chain. A control cost penalizing KL divergence between controlled and uncontrolled transition probabilities makes the minimization problem convex, and allows analytical computation of the optimal controls given the optimal value function. An exponential transformation of the optimal value function makes the minimized Bellman equation linear. Apart from their theoretical significance, the new MDPs enable efficient approximations to traditional MDPs. Shortest path problems are approximated to arbitrary precision with largest eigenvalue problems, yielding an O (n) algorithm. Accurate approximations to generic MDPs are obtained via continuous embedding reminiscent of LP relaxation in integer programming. Off-policy learning of the optimal value function is possible without need for state-action values; the new algorithm (Z-learning) outperforms Q-learning. This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MDPs can grow exponentially in the representation size. In this paper, we present two approximate solution algorithms that exploit structure in factored MDPs. Both use an approximate value function represented as a linear combination of basis functions, where each basis function involves only a small subset of the domain variables. A key contribution of this paper is that it shows how the basic operations of both algorithms can be performed efficiently in closed form, by exploiting both additive and context-specific structure in a factored MDP. A central element of our algorithms is a novel linear program decomposition technique, analogous to variable elimination in Bayesian networks, which reduces an exponentially large LP to a provably equivalent, polynomial-sized one. One algorithm uses approximate linear programming, and the second approximate dynamic programming. Our dynamic programming algorithm is novel in that it uses an approximation based on max-norm, a technique that more directly minimizes the terms that appear in error bounds for approximate MDP algorithms. We provide experimental results on problems with over 1040 states, demonstrating a promising indication of the scalability of our approach, and compare our algorithm to an existing state-of-the-art approach, showing, in some problems, exponential gains in computation time. Although many real-world stochastic planning problems are more naturally formulated by hybrid models with both discrete and continuous variables, current state-of-the-art methods cannot adequately address these problems. We present the first framework that can exploit problem structure for modeling and solving hybrid problems efficiently. We formulate these problems as hybrid Markov decision processes (MDPs with continuous and discrete state and action variables), which we assume can be represented in a factored way using a hybrid dynamic Bayesian network (hybrid DBN). This formulation also allows us to apply our methods to collaborative multiagent settings. We present a new linear program approximation method that exploits the structure of the hybrid MDP and lets us compute approximate value functions more efficiently. In particular, we describe a new factored discretization of continuous variables that avoids the exponential blow-up of traditional approaches. We provide theoretical bounds on the quality of such an approximation and on its scale-up potential. We support our theoretical arguments with experiments on a set of control problems with up to 28-dimensional continuous state space and 22-dimensional action space. A popular approach for online decision making in large MDPs is time-bounded tree search. The effectiveness of tree search, however, is largely influenced by the action branching factor, which limits the search depth given a time bound. An obvious way to reduce action branching is to consider only a subset of potentially good actions at each state as specified by a provided partial policy. In this work, we consider offline learning of such partial policies with the goal of speeding up search without significantly reducing decision-making quality. Our first contribution is to study learning algorithms based on reducing our learning problem to i.i.d. supervised learning. We give a reduction-style analysis of three such algorithms, each making different assumptions, which relates the supervised learning objectives to the sub-optimality of search using the learned partial policies. Our second contribution is to describe concrete implementations of the algorithms within the popular framework of Monte-Carlo tree search. Finally, the third contribution is to evaluate the learning algorithms in two challenging MDPs with large action branching factors, showing that the learned partial policies can significantly improve the anytime performance of Monte-Carlo tree search.