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.

Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficient relational variational inference algorithm that factors largescale probability models into simpler variational models, composed of mixtures of iid (Bernoulli) random variables. The algorithm takes probability relational models of largescale hybrid systems and converts them to a close-to-optimal variational models. Then, it efficiently calculates marginal probabilities on the variational models by using a latent (or lifted) variable elimination or a lifted stochastic sampling. This inference is unique because it maintains the relational structure upon individual observations and during inference steps.

Agents learning to act autonomously in real-world domains must acquire a model of the dynamics of the domain in which they operate. Learning domain dynamics can be challenging, especially where an agent only has partial access to the world state, and/or noisy external sensors. Even in standard STRIPS domains, existing approaches cannot learn from noisy, incomplete observations typical of real-world domains. We propose a method which learns STRIPS action models in such domains, by decomposing the problem into first learning a transition function between states in the form of a set of classifiers, and then deriving explicit STRIPS rules from the classifiers' parameters. We evaluate our approach on simulated standard planning domains from the International Planning Competition, and show that it learns useful domain descriptions from noisy, incomplete observations.

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items are scored independently by their similarity to the query in the latent embedding space. The structure of the ranked list (i.e. considering the set of items returned as a whole) is not taken into account. This can be a problem because the set of top predictions can be either too diverse (contain results that contradict each other) or are not diverse enough. In this paper we introduce a method for learning latent structured rankings that improves over existing methods by providing the right blend of predictions at the top of the ranked list. Particular emphasis is put on making this method scalable. Empirical results on large scale image annotation and music recommendation tasks show improvements over existing approaches.

We introduce a method to learn a mixture of submodular "shells" in a large-margin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantiated to produce a more complex submodular function. What our algorithm learns are the mixture weights over such shells. We provide a risk bound guarantee when learning in a large-margin structured-prediction setting using a projected subgradient method when only approximate submodular optimization is possible (such as with submodular function maximization). We apply this method to the problem of multi-document summarization and produce the best results reported so far on the widely used NIST DUC-05 through DUC-07 document summarization corpora.

Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is well-understood, with efficient computations taking O(DlogD) time. Yet efficient marginalization and sampling have not been addressed as thoroughly in the machine learning community. We show that there exists a simple algorithm for computing marginal probabilities and drawing exact joint samples that runs in O(Dlog2 D) time, and we show how to frame the algorithm as efficient belief propagation in a low order tree-structured model that includes additional auxiliary variables. We then develop a new, more general class of models, termed Recursive Cardinality models, which take advantage of this efficiency. Finally, we show how to do efficient exact inference in models composed of a tree structure and a cardinality potential. We explore the expressive power of Recursive Cardinality models and empirically demonstrate their utility.

Previous work on recommender systems mainly focus on fitting the ratings provided by users. However, the response patterns, i.e., some items are rated while others not, are generally ignored. We argue that failing to observe such response patterns can lead to biased parameter estimation and sub-optimal model performance. Although several pieces of work have tried to model users' response patterns, they miss the effectiveness and interpretability of the successful matrix factorization collaborative filtering approaches. To bridge the gap, in this paper, we unify explicit response models and PMF to establish the Response Aware Probabilistic Matrix Factorization (RAPMF) framework. We show that RAPMF subsumes PMF as a special case. Empirically we demonstrate the merits of RAPMF from various aspects.

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.

Active Learning (AL) is increasingly important in a broad range of applications. Two main AL principles to obtain accurate classification with few labeled data are refinement of the current decision boundary and exploration of poorly sampled regions. In this paper we derive a novel AL scheme that balances these two principles in a natural way. In contrast to many AL strategies, which are based on an estimated class conditional probability ^p(y|x), a key component of our approach is to view this quantity as a random variable, hence explicitly considering the uncertainty in its estimated value. Our main contribution is a novel mathematical framework for uncertainty-based AL, and a corresponding AL scheme, where the uncertainty in ^p(y|x) is modeled by a second-order distribution. On the practical side, we show how to approximate such second-order distributions for kernel density classification. Finally, we find that over a large number of UCI, USPS and Caltech4 datasets, our AL scheme achieves significantly better learning curves than popular AL methods such as uncertainty sampling and error reduction sampling, when all use the same kernel density classifier.

Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in social sciences and marketing, "analytical ability" in educational testing, or "inflation" in economics). This leads to the development of measurement instruments to record noisy indirect evidence for such unobserved variables such as surveys, tests and price indexes. In such problems, there are postulated latent variables and a given measurement model. At the same time, other unantecipated latent variables can add further unmeasured confounding to the observed variables. The problem is how to deal with unantecipated latents variables. In this paper, we provide a method loosely inspired by canonical correlation that makes use of background information concerning the "known" latent variables. Given a partially specified structure, it provides a structure learning approach to detect "unknown unknowns," the confounding effect of potentially infinitely many other latent variables. This is done without explicitly modeling such extra latent factors. Because of the special structure of the problem, we are able to exploit a new variation of composite likelihood fitting to efficiently learn this structure. Validation is provided with experiments in synthetic data and the analysis of a large survey done with a sample of over 100,000 staff members of the National Health Service of the United Kingdom.