Partially Observable Markov Decision Processes (pO"MOPs) constitute an important class of reinforcement learning problems which present unique theoretical and computational difficulties. In the absence of the Markov property, popular reinforcement learning algorithms such as Q-Iearning may no longer be effective, and memory-based methods which remove partial observability via state-estimation are notoriously expensive. An alternative approach is to seek a stochastic memoryless policy which for each observation of the environment prescribes a probability distribution over available actions that maximizes the average reward per timestep. A reinforcement learning algorithm which learns a locally optimal stochastic memoryless policy has been proposed by Jaakkola, Singh and Jordan, but not empirically verified. We present a variation of this algorithm, discuss its implementation, and demonstrate its viability using four test problems.

We describe Maximum-Likelihood Continuity Mapping (MALCOM), an alternative to hidden Markov models (HMMs) for processing sequence data such as speech. While HMMs have a discrete "hidden" space constrained bya fixed finite-automaton architecture, MALCOM has a continuous hidden space-a continuity map-that is constrained only by a smoothness requirement on paths through the space. MALCOM fits into the same probabilistic framework for speech recognition as HMMs, but it represents a more realistic model of the speech production process. To evaluate the extent to which MALCOM captures speech production information, we generated continuous speech continuity maps for three speakers and used the paths through them to predict measured speech articulator data. The median correlation between the MALCOM paths obtained from only the speech acoustics and articulator measurements was 0.77 on an independent test set not used to train MALCOM or the predictor.

The Expectation-Maximization (EM) algorithm is an iterative procedure formaximum likelihood parameter estimation from data sets with missing or hidden variables [2]. It has been applied to system identification in linear stochastic state-space models, where the state variables are hidden from the observer and both the state and the parameters of the model have to be estimated simultaneously [9].We present a generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems. The "expectation" stepmakes use of Extended Kalman Smoothing to estimate the state, while the "maximization" step re-estimates the parameters usingthese uncertain state estimates. In general, the nonlinear maximization step is difficult because it requires integrating out the uncertainty in the states. However, if Gaussian radial basis function (RBF)approximators are used to model the nonlinearities, the integrals become tractable and the maximization step can be solved via systems of linear equations.

Since BLHT learns a stochastic model based on Bayesian Learning, the overfitting problemis reasonably solved. Moreover, BLHT has an efficient implementation. This paper shows that the model learned by BLHT converges toone which provides the most accurate predictions of percepts and rewards, given short-term memory. 1 INTRODUCTION Research on Reinforcement Learning (RL) problem forpartially observable environments is gaining more attention recently. This is mainly because the assumption that perfect and complete perception of the state of the environment is available for the learning agent, which many previous RL algorithms require, is not valid for many realistic environments.

Graphical models provide a broad probabilistic framework with applications inspeech recognition (Hidden Markov Models), medical diagnosis (Belief networks) and artificial intelligence (Boltzmann Machines). However, the computing time is typically exponential in the number of nodes in the graph. Within the variational framework forapproximating these models, we present two classes of distributions, decimatableBoltzmann Machines and Tractable Belief Networks that go beyond the standard factorized approach. We give generalised mean-field equations for both these directed and undirected approximations. Simulation results on a small benchmark problemsuggest using these richer approximations compares favorably against others previously reported in the literature. 1 Introduction Graphical models provide a powerful framework for probabilistic inference[l] but suffer intractability when applied to large scale problems.

To formulate a probabilistic model of this process, we consider two variables-one continuous (x), one discrete (s)-that evolve jointly in time. Thus the vector x traces out a smooth multidimensional curve, to each point of which the variable s attaches a discrete label. Markov processes on curves are based on the concept of arc length. After reviewing how to compute arc lengths along curves, we introduce a family of Markov processes whose predictions are invariant to nonlinear warpings of time. We then consider the ways in which these processes (and various generalizations) differ from HMMs. Markov Processes on Curves for Automatic Speech Recognition 753 2.1 Arc length Let g() define a D x D matrix-valued function over x E RP. If g() is everywhere nonnegative definite, then we can use it as a metric to compute distances along curves.

We introduce a novel framework for simultaneous structure and parameter learning in hidden-variable conditional probability models, based on an entropic prior and a solution for its maximum a posteriori (MAP) estimator. The MAP estimate minimizes uncertainty in all respects: cross-entropy between model and data; entropy of the model; entropy of the data's descriptive statistics. Iterative estimation extinguishes weakly supported parameters, compressing and sparsifying the model. Trimming operators accelerate this process by removing excess parameters and, unlike most pruning schemes, guarantee an increase in posterior probability. Entropic estimation takes a overcomplete random model and simplifies it, inducing the structure of relations between hidden and observed variables. Applied to hidden Markov models (HMMs), it finds a concise finite-state machine representing the hidden structure of a signal. We entropically model music, handwriting, and video time-series, and show that the resulting models are highly concise, structured, predictive, and interpretable: Surviving states tend to be highly correlated with meaningful partitions of the data, while surviving transitions provide a low-perplexity model of the signal dynamics.

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Classifier systems are now viewed disappointing because of their problems suchas the rule strength vs rule set performance problem and the credit assignment problem. In order to solve the problems, we have developed ahybrid classifier system: GLS (Generalization Learning System). In designing GLS, we view CSs as model free learning in POMDPs and take a hybrid approach to finding the best generalization, given the total number of rules. GLS uses the policy improvement procedure by Jaakkola et al. for an locally optimal stochastic policy when a set of rule conditions is given. GLS uses GA to search for the best set of rule conditions. 1 INTRODUCTION Classifier systems (CSs) (Holland 1986) have been among the most used in reinforcement learning.

A simple learning rule is derived, the VAPS algorithm, which can be instantiated to generate a wide range of new reinforcementlearning algorithms.These algorithms solve a number of open problems, define several new approaches to reinforcement learning, and unify different approaches to reinforcement learning under a single theory. These algorithms all have guaranteed convergence, and include modifications of several existing algorithms that were known to fail to converge on simple MOPs. These include Q learning, SARSA, and advantage learning. In addition to these value-based algorithms it also generates pure policy-search reinforcement-learning algorithms, which learn optimal policies without learning a value function. In addition, it allows policysearch andvalue-based algorithms to be combined, thus unifying two very different approaches to reinforcement learning into a single Value and Policy Search (V APS) algorithm.