We show that the λ-return target used in the TD(λ) family of algorithms is the maximum likelihood estimator for a specific model of how the variance of an n-step return estimate increases with n.

We present a new algorithm for exactly solving decision-making problems represented as an influence diagram. We do not require the usual assumptions of no forgetting and regularity, which allows us to solve problems with limited information.

POMDP planning faces two major computational challenges: large state spaces and long planning horizons. The recently introduced Monte Carlo Value Iteration (MCVI) can tackle POMDPs with very large discrete state spaces or continuous state spaces, but its performance degrades when faced with long planning horizons. This paper presents Macro-MCVI, which extends MCVI by exploiting macro-actions for temporal abstraction. We provide sufficient conditions for Macro-MCVI to inherit the good theoretical properties of MCVI. Macro-MCVI does not require explicit construction of probabilistic models for macro-actions and is thus easy to apply in practice. Experiments show that Macro-MCVI substantially improves the performance of MCVI with suitable macro-actions.

Most existing Multiple-Instance Learning (MIL) algorithms assume data instances and/or data bags are independently and identically distributed. But there often exists rich additional dependency/structure information between instances/bags within many applications of MIL. Ignoring this structure information limits the performance of existing MIL algorithms. This paper explores the research problem as multiple instance learning on structured data (MILSD) and formulates a novel framework that considers additional structure information. In particular, an effective and efficient optimization algorithm has been proposed to solve the original non-convex optimization problem by using a combination of Concave-Convex Constraint Programming (CCCP) method and an adapted Cutting Plane method, which deals with two sets of constraints caused by learning on instances within individual bags and learning on structured data. Our method has the nice convergence property, with specified precision on each set of constraints. Experimental results on three different applications, i.e., webpage classification, market targeting, and protein fold identification, clearly demonstrate the advantages of the proposed method over state-of-the-art methods.

An important task in exploring and analyzing real-world data sets is to detect unusual and interesting phenomena. In this paper, we study the group anomaly detection problem. Unlike traditional anomaly detection research that focuses on data points, our goal is to discover anomalous aggregated behaviors of groups of points. For this purpose, we propose the Flexible Genre Model (FGM). FGM is designed to characterize data groups at both the point level and the group level so as to detect various types of group anomalies. We evaluate the effectiveness of FGM on both synthetic and real data sets including images and turbulence data, and show that it is superior to existing approaches in detecting group anomalies.

Log-linear models are widely used probability models for statistical pattern recognition. Typically, log-linear models are trained according to a convex criterion. In recent years, the interest in log-linear models has greatly increased. The optimization of log-linear model parameters is costly and therefore an important topic, in particular for large-scale applications. Different optimization algorithms have been evaluated empirically in many papers. In this work, we analyze the optimization problem analytically and show that the training of log-linear models can be highly ill-conditioned. We verify our findings on two handwriting tasks. By making use of our convergence analysis, we obtain good results on a large-scale continuous handwriting recognition task with a simple and generic approach.

We consider the problem of Bayesian inference for continuous-time multi-stable stochastic systems which can change both their diffusion and drift parameters at discrete times. We propose exact inference and sampling methodologies for two specific cases where the discontinuous dynamics is given by a Poisson process and a two-state Markovian switch. We test the methodology on simulated data, and apply it to two real data sets in finance and systems biology. Our experimental results show that the approach leads to valid inferences and non-trivial insights.

The performance of Markov chain Monte Carlo methods is often sensitive to the scaling and correlations between the random variables of interest. An important source of information about the local correlation and scale is given by the Hessian matrix of the target distribution, but this is often either computationally expensive or infeasible. In this paper we propose MCMC samplers that make use of quasi-Newton approximations, which approximate the Hessian of the target distribution from previous samples and gradients generated by the sampler. A key issue is that MCMC samplers that depend on the history of previous states are in general not valid. We address this problem by using limited memory quasi-Newton methods, which depend only on a fixed window of previous samples. On several real world datasets, we show that the quasi-Newton sampler is more effective than standard Hamiltonian Monte Carlo at a fraction of the cost of MCMC methods that require higher-order derivatives.

Factored Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) form a powerful framework for multiagent planning under uncertainty, but optimal solutions require a rigid history-based policy representation. In this paper we allow inter-agent communication which turns the problem in a centralized Multiagent POMDP (MPOMDP). We map belief distributions over state factors to an agent's local actions by exploiting structure in the joint MPOMDP policy. The key point is that when sparse dependencies between the agents' decisions exist, often the belief over its local state factors is sufficient for an agent to unequivocally identify the optimal action, and communication can be avoided. We formalize these notions by casting the problem into convex optimization form, and present experimental results illustrating the savings in communication that we can obtain.

The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are possible if all beliefs are Gaussian processes. A first order approximation of learning of both loss and dynamics, for nonlinear, time-varying systems in continuous time and space, subject to a relatively weak restriction on the dynamics, is described by an infinite-dimensional partial differential equation. An approximate finitedimensional projection gives an impression for how this result may be helpful.