Increasing attention has been paid to reinforcement learning algorithms inrecent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of non-Markov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a Monte-Carlo policy evaluationcombined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerablybetter than any deterministic policy. Although the space of stochastic policies is continuous-even for a discrete action space-our algorithm is computationally tractable.

It is widely accepted that the use of more compact representations than lookup tables is crucial to scaling reinforcement learning (RL) algorithms to real-world problems. Unfortunately almost all of the theory of reinforcement learning assumes lookup table representations. Inthis paper we address the pressing issue of combining function approximation and RL, and present 1) a function approximator basedon a simple extension to state aggregation (a commonly used form of compact representation), namely soft state aggregation, 2) a theory of convergence for RL with arbitrary, but fixed, soft state aggregation, 3) a novel intuitive understanding of the effect of state aggregation on online RL, and 4) a new heuristic adaptive state aggregation algorithm that finds improved compact representations by exploiting the non-discrete nature of soft state aggregation. Preliminary empirical results are also presented.

It is widely accepted that the use of more compact representations than lookup tables is crucial to scaling reinforcement learning (RL) algorithms to real-world problems. Unfortunately almost all of the theory of reinforcement learning assumes lookup table representations. In this paper we address the pressing issue of combining function approximation and RL, and present 1) a function approximator based on a simple extension to state aggregation (a commonly used form of compact representation), namely soft state aggregation, 2) a theory of convergence for RL with arbitrary, but fixed, soft state aggregation, 3) a novel intuitive understanding of the effect of state aggregation on online RL, and 4) a new heuristic adaptive state aggregation algorithm that finds improved compact representations by exploiting the non-discrete nature of soft state aggregation. Preliminary empirical results are also presented.

Increasing attention has been paid to reinforcement learning algorithms in recent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of non-Markov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a Monte-Carlo policy evaluation combined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerably better than any deterministic policy. Although the space of stochastic policies is continuous-even for a discrete action space-our algorithm is computationally tractable.

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learning problems involving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DPbased learning algorithms to the powerful techniques of stochastic approximation via a new convergence theorem, enabling us to establish a class of convergent algorithms to which both TD("\) and Q-Iearning belong. 1 INTRODUCTION Learning to predict the future and to find an optimal way of controlling it are the basic goals of learning systems that interact with their environment. A variety of algorithms are currently being studied for the purposes of prediction and control in incompletely specified, stochastic environments. Here we consider learning algorithms defined in Markov environments. There are actions or controls (u) available for the learner that affect both the state transition probabilities, and the probability distribution for the immediate, state dependent costs (Ci(u)) incurred by the learner.

While exploring to find better solutions, an agent performing online reinforcementlearning (RL) can perform worse than is acceptable. Insome cases, exploration might have unsafe, or even catastrophic, results,often modeled in terms of reaching'failure' states of the agent's environment. This paper presents a method that uses domain knowledge to reduce the number of failures during exploration. Thismethod formulates the set of actions from which the RL agent composes a control policy to ensure that exploration is conducted in a policy space that excludes most of the unacceptable policies. The resulting action set has a more abstract relationship to the task being solved than is common in many applications of RL. Although the cost of this added safety is that learning may result in a suboptimal solution, we argue that this is an appropriate tradeoffin many problems. We illustrate this method in the domain of motion planning. "'This work was done while the first author was finishing his Ph.D in computer science at the University of Massachusetts, Amherst.

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learning problems involving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DPbased learning algorithms to the powerful techniques of stochastic approximation via a new convergence theorem, enabling us to establish a class of convergent algorithms to which both TD("\) and Q-Iearning belong. 1 INTRODUCTION Learning to predict the future and to find an optimal way of controlling it are the basic goals of learning systems that interact with their environment. A variety of algorithms are currently being studied for the purposes of prediction and control in incompletely specified, stochastic environments. Here we consider learning algorithms defined in Markov environments. There are actions or controls (u) available for the learner that affect both the state transition probabilities, and the probability distribution for the immediate, state dependent costs (Ci(u)) incurred by the learner.

While exploring to find better solutions, an agent performing online reinforcement learning (RL) can perform worse than is acceptable. In some cases, exploration might have unsafe, or even catastrophic, results, often modeled in terms of reaching'failure' states of the agent's environment. This paper presents a method that uses domain knowledge to reduce the number of failures during exploration. This method formulates the set of actions from which the RL agent composes a control policy to ensure that exploration is conducted in a policy space that excludes most of the unacceptable policies. The resulting action set has a more abstract relationship to the task being solved than is common in many applications of RL. Although the cost of this added safety is that learning may result in a suboptimal solution, we argue that this is an appropriate tradeoff in many problems. We illustrate this method in the domain of motion planning. "'This work was done while the first author was finishing his Ph.D in computer science at the University of Massachusetts, Amherst.

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learning problemsinvolving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DPbased learning algorithms to the powerful techniquesof stochastic approximation via a new convergence theorem, enabling us to establish a class of convergent algorithms to which both TD("\) and Q-Iearning belong. 1 INTRODUCTION Learning to predict the future and to find an optimal way of controlling it are the basic goals of learning systems that interact with their environment. A variety of algorithms are currently being studied for the purposes of prediction and control in incompletely specified, stochastic environments. Here we consider learning algorithms definedin Markov environments. There are actions or controls (u) available for the learner that affect both the state transition probabilities, and the probability distributionfor the immediate, state dependent costs (Ci( u)) incurred by the learner.

I present a modular network architecture and a learning algorithm based on incremental dynamic programming that allows a single learning agent to learn to solve multiple Markovian decision tasks (MDTs) with significant transfer of learning across the tasks. I consider a class of MDTs, called composite tasks, formed by temporally concatenating a number of simpler, elemental MDTs. The architecture is trained on a set of composite and elemental MDTs. The temporal structure of a composite task is assumed to be unknown and the architecture learns to produce a temporal decomposition. It is shown that under certain conditions the solution of a composite MDT can be constructed by computationally inexpensive modifications of the solutions of its constituent elemental MDTs. 1 INTRODUCTION Most applications of domain independent learning algorithms have focussed on learning single tasks. Building more sophisticated learning agents that operate in complex environments will require handling multiple tasks/goals (Singh, 1992). Research effort on the scaling problem has concentrated on discovering faster learning algorithms, and while that will certainly help, techniques that allow transfer of learning across tasks will be indispensable for building autonomous learning agents that have to learn to solve multiple tasks. In this paper I consider a learning agent that interacts with an external, finite-state, discrete-time, stochastic dynamical environment and faces multiple sequences of Markovian decision tasks (MDTs).