The information bottleneck method is an unsupervised model independent data organization technique. Given a joint distribution peA, B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. In a recent paper, we introduced a general principled framework for multivariate extensions of the information bottleneck method that allows us to consider multiple systems of data partitions that are interrelated. In this paper, we present a new family of simple agglomerative algorithms to construct such systems of interrelated clusters. We analyze the behavior of these algorithms and apply them to several real-life datasets.

It has been noted by several authors that Belief Propagation can can also give impressive results for graphs that are not trees [2]. The Cluster Variation Method (CVM), is a method that has been developed in the physics community for approximate inference in the Ising model [3]. The CVM approximates the joint probability distribution by a number of (overlapping) marginal distributions (clusters). The quality of the approximation is determined by the size and number of clusters. When the clusters consist of only two variables, the method is known as the Bethe approximation.

We discuss the problem of ranking instances. In our framework each instance is associated with a rank or a rating, which is an integer from 1 to k. Our goal is to find a rank-prediction rule that assigns each instance a rank which is as close as possible to the instance's true rank. We describe a simple and efficient online algorithm, analyze its performance in the mistake bound model, and prove its correctness. We describe two sets of experiments, with synthetic data and with the EachMovie dataset for collaborative filtering.

We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

We consider the problem of learning to attain multiple goals in a dynamic environment, which is initially unknown. In addition, the environment may contain arbitrarily varying elements related to actions of other agents or to non-stationary moves of Nature. This problem is modelled as a stochastic (Markov) game between the learning agent and an arbitrary player, with a vector-valued reward function. The objective of the learning agent is to have its long-term average reward vector belong to a given target set. We devise an algorithm for achieving this task, which is based on the theory of approachability for stochastic games. This algorithm combines, in an appropriate way, a finite set of standard, scalar-reward learning algorithms. Sufficient conditions are given for the convergence of the learning algorithm to a general target set. The specialization of these results to the single-controller Markov decision problem are discussed as well.

We propose a new approach to reinforcement learning which combines least squares function approximation with policy iteration. Our method is model-free and completely off policy. We are motivated by the least squares temporal difference learning algorithm (LSTD), which is known for its efficient use of sample experiences compared to pure temporal difference algorithms. LSTD is ideal for prediction problems, however it heretofore has not had a straightforward application to control problems. Moreover, approximations learned by LSTD are strongly influenced by the visitation distribution over states.

We provide a natural gradient method that represents the steepest descent direction based on the underlying structure of the parameter space. Although gradient methods cannot make large changes in the values of the parameters, we show that the natural gradient is moving toward choosing a greedy optimal action rather than just a better action. These greedy optimal actions are those that would be chosen under one improvement step of policy iteration with approximate, compatible value functions, as defined by Sutton et al. [9]. We then show drastic performance improvements in simple MDPs and in the more challenging MDP of Tetris. 1 Introduction There has been a growing interest in direct policy-gradient methods for approximate planning in large Markov decision problems (MDPs). Unfortunately, the standard gradient descent rule is noncovariant.

We present a principled and efficient planning algorithm for cooperative multiagent dynamic systems. A striking feature of our method is that the coordination and communication between the agents is not imposed, but derived directly from the system dynamics and function approximation architecture. We view the entire multiagent system as a single, large Markov decision process (MDP), which we assume can be represented in a factored way using a dynamic Bayesian network (DBN). The action space of the resulting MDP is the joint action space of the entire set of agents. Our approach is based on the use of factored linear value functions as an approximation to the joint value function.

The first is the widely used optimistic Q-learning, which initializes the Q-values to large initial values and then follows a greedy policy with respect to the Q-values. We show that setting the initial value sufficiently large guarantees the converges to an E optimal policy. The second is a new and novel algorithm incremental Q-learning, which gradually promotes the values of actions that are not taken. We show that incremental Q-learning converges, in the limit, to the optimal policy. Our incremental Q-learning algorithm can be viewed as derandomization of the E-greedy Q-learning. 1 Introduction One of the challenges of Reinforcement Learning is learning in an unknown environment.

This paper presents reinforcement learning with a Long Short Term Memory recurrent neural network: RL-LSTM. Model-free RL-LSTM using Advantage(,x) learning and directed exploration can solve non-Markovian tasks with long-term dependencies between relevant events. This is demonstrated in a T-maze task, as well as in a difficult variation of the pole balancing task. 1 Introduction Reinforcement learning (RL) is a way of learning how to behave based on delayed reward signals [12]. Among the more important challenges for RL are tasks where part of the state of the environment is hidden from the agent. Such tasks are called non-Markovian tasks or Partially Observable Markov Decision Processes. Many real world tasks have this problem of hidden state. For instance, in a navigation task different positions in the environment may look the same, but one and the same action may lead to different next states or rewards. Thus, hidden state makes RL more realistic.