We present an application of hierarchical Bayesian estimation to robot map building. The revisiting problem occurs when a robot has to decide whether it is seeing a previously-built portion of a map, or is exploring new territory. This is a difficult decision problem, requiring the probability of being outside of the current known map. To estimate this probability, we model the structure of a "typical" environment as a hidden Markov model that generates sequences of views observed by a robot navigating through the environment. A Dirichlet prior over structural models is learned from previously explored environments. Whenever a robot explores a new environment, the posterior over the model is estimated by Dirichlet hyperparameters. Our approach is implemented and tested in the context of multi-robot map merging, a particularly difficult instance of the revisiting problem. Experiments with robot data show that the technique yields strong improvements over alternative methods.

For a given problem, the optimal Markov policy can be considerred as a conditional or contingent plan containing a (potentially large) number of branches. Unfortunately, there are applications where it is desirable to strictly limit the number of decision points and branches in a plan. For example, it may be that plans must later undergo more detailed simulation to verify correctness and safety, or that they must be simple enough to be understood and analyzed by humans. As a result, it may be necessary to limit consideration to plans with only a small number of branches. This raises the question of how one goes about finding optimal plans containing only a limited number of branches. In this paper, we present an any-time algorithm for optimal k-contingency planning (OKP). It is the first optimal algorithm for limited contingency planning that is not an explicit enumeration of possible contingent plans. By modelling the problem as a Partially Observable Markov Decision Process, it implements the Bellman optimality principle and prunes the solution space. We present experimental results of applying this algorithm to some simple test cases.

This paper presents a scalable control algorithm that enables a deployed mobile robot to make high-level control decisions under full consideration of its probabilistic belief. We draw on insights from the rich literature of structured robot controllers and hierarchical MDPs to propose PolCA, a hierarchical probabilistic control algorithm which learns both subtask-specific state abstractions and policies. The resulting controller has been successfully implemented onboard a mobile robotic assistant deployed in a nursing facility. To the best of our knowledge, this work is a unique instance of applying POMDPs to highlevel robotic control problems.

This paper examines a number of solution methods for decision processes with non-Markovian rewards (NMRDPs). They all exploit a temporal logic specification of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable to well-known MDP solution methods. They differ however in the representation of the target MDP and the class of MDP solution methods to which they are suited. As a result, they adopt different temporal logics and different translations. Unfortunately, no implementation of these methods nor experimental let alone comparative results have ever been reported. This paper is the first step towards filling this gap. We describe an integrated system for solving NMRDPs which implements these methods and several variants under a common interface; we use it to compare the various approaches and identify the problem features favoring one over the other.

Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy. However, belief propagation does not always converge, which explains the need for approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP and UPS. Here we describe a class of algorithms that solves this typically nonconvex constrained minimization of the Kikuchi free energy through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speed-ups over CCCP.

We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of {m P}{cal C}+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.

Symbolic representations have been used successfully in off-line planning algorithms for Markov decision processes. We show that they can also improve the performance of on-line planners. In addition to reducing computation time, symbolic generalization can reduce the amount of costly real-world interactions required for convergence. We introduce Symbolic Real-Time Dynamic Programming (or sRTDP), an extension of RTDP. After each step of on-line interaction with an environment, sRTDP uses symbolic model-checking techniques to generalizes its experience by updating a group of states rather than a single state. We examine two heuristic approaches to dynamic grouping of states and show that they accelerate the planning process significantly in terms of both CPU time and the number of steps of interaction with the environment.

Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributions. DNs are very fast to learn, but the conditional distributions may be inconsistent with each other and few inference algorithms support DNs. In this paper, we present a closed-form method for converting a DN into an MN, allowing us to enjoy both the efficiency of DN learning and the convenience of the MN representation. When the DN is consistent, this conversion is exact. For inconsistent DNs, we present averaging methods that significantly improve the approximation. In experiments on 12 standard datasets, our methods are orders of magnitude faster than and often more accurate than combining conditional distributions using weight learning.

This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to minimization of convex functions in highdimensional spaces. Unlike traditional gradient methods, mirror descent undertakes gradient updates of weights in both the dual space and primal space, which are linked together using a Legendre transform. Mirror descent can be viewed as a proximal algorithm where the distance generating function used is a Bregman divergence. A new class of proximal-gradient based temporal-difference (TD) methods are presented based on different Bregman divergences, which are more powerful than regular TD learning. Examples of Bregman divergences that are studied include p-norm functions, and Mahalanobis distance based on the covariance of sample gradients. A new family of sparse mirror-descent reinforcement learning methods are proposed, which are able to find sparse fixed points of an l1-regularized Bellman equation at significantly less computational cost than previous methods based on second-order matrix methods. An experimental study of mirror-descent reinforcement learning is presented using discrete and continuous Markov decision processes.

Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arising from multiple modalities or make restrictive assumptions about the form of the functions or transformations, limiting their generality. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is determined in a data-driven fashion through the use of a Dirichlet process prior, and it can accommodate any transformation function parameterized by a continuous parameter vector. As a result, it is applicable to a wide range of data types, and transformation functions. We present positive results on synthetic two-dimensional data, on a set of one-dimensional curves, and on various image data sets, showing large improvements over previous work. We discuss several variations of the model and conclude with directions for future work.