Markov control algorithms that perform smooth, non-greedy updates of the policy have been shown to be very general and versatile, with policy gradient and Expectation Maximisation algorithms being particularly popular. For these algorithms, marginal inference of the reward weighted trajectory distribution is required to perform policy updates. We discuss a new exact inference algorithm for these marginals in the finite horizon case that is more efficient than the standard approach based on classical forward-backward recursions. We also provide a principled extension to infinite horizon Markov Decision Problems that explicitly accounts for an infinite horizon. This extension provides a novel algorithm for both policy gradients and Expectation Maximisation in infinite horizon problems.

Markov decision processes (MDPs) are widely used in modeling decision making problems in stochastic environments. However, precise specification of the reward functions in MDPs is often very difficult. Recent approaches have focused on computing an optimal policy based on the minimax regret criterion for obtaining a robust policy under uncertainty in the reward function. One of the core tasks in computing the minimax regret policy is to obtain the set of all policies that can be optimal for some candidate reward function. In this paper, we propose an efficient algorithm that exploits the geometric properties of the reward function associated with the policies. We also present an approximate version of the method for further speed up. We experimentally demonstrate that our algorithm improves the performance by orders of magnitude.

We consider how to use the Bellman residual of the dynamic programming operator to compute suboptimality bounds for solutions to stochastic shortest path problems. Such bounds have been previously established only in the special case that "all policies are proper," in which case the dynamic programming operator is known to be a contraction, and have been shown to be easily computable only in the more limited special case of discounting. Under the condition that transition costs are positive, we show that suboptimality bounds can be easily computed even when not all policies are proper. In the general case when there are no restrictions on transition costs, the analysis is more complex. But we present preliminary results that show such bounds are possible.

In this paper, we develop a qualitative theory of influence diagrams that can be used to model and solve sequential decision making tasks when only qualitative (or imprecise) information is available. Our approach is based on an order-of-magnitude approximation of both probabilities and utilities and allows for specifying partially ordered preferences via sets of utility values. We also propose a dedicated variable elimination algorithm that can be applied for solving order-of-magnitude influence diagrams.

Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the hierarchical clustering problem, which arises in a variety of domains including biology, sensor networks and decision making in operational research. We derive an inference algorithm that operates by propagating information up and down the hierarchy, and is efficient despite the high-order potentials required for the graphical model formulation. We demonstrate that our method outperforms greedy techniques that cluster one layer at a time. We show that on an artificial dataset designed to mimic the HIV-strain mutation dynamics, our method outperforms related methods. For real HIV sequences, where the ground truth is not available, we show our method achieves better results, in terms of the underlying objective function, and show the results correspond meaningfully to geographical location and strain subtypes. Finally we report results on using the method for the analysis of mass spectra, showing it performs favorably compared to state-of-the-art methods.

We propose a method called EDML for learning MAP parameters in binary Bayesian networks under incomplete data. The method assumes Beta priors and can be used to learn maximum likelihood parameters when the priors are uninformative. EDML exhibits interesting behaviors, especially when compared to EM. We introduce EDML, explain its origin, and study some of its properties both analytically and empirically.

The ideas about decision making under ignorance in economics are combined with the ideas about uncertainty representation in computer science. The combination sheds new light on the question of how artificial agents can act in a dynamically consistent manner. The notion of sequential consistency is formalized by adapting the law of iterated expectation for plausibility measures. The necessary and sufficient condition for a certainty equivalence operator for Nehring-Puppe's preference to be sequentially consistent is given. This result sheds light on the models of decision making under uncertainty.

Previous work has shown that the problem of learning the optimal structure of a Bayesian network can be formulated as a shortest path finding problem in a graph and solved using A* search. In this paper, we improve the scalability of this approach by developing a memory-efficient heuristic search algorithm for learning the structure of a Bayesian network. Instead of using A*, we propose a frontier breadth-first branch and bound search that leverages the layered structure of the search graph of this problem so that no more than two layers of the graph, plus solution reconstruction information, need to be stored in memory at a time. To further improve scalability, the algorithm stores most of the graph in external memory, such as hard disk, when it does not fit in RAM. Experimental results show that the resulting algorithm solves significantly larger problems than the current state of the art.

Approximate Bayesian inference is NP-hard. Dagum and Luby defined the Local Variance Bound (LVB) to measure the approximation hardness of Bayesian inference on Bayesian networks, assuming the networks model strictly positive joint probability distributions, i.e. zero probabilities are not permitted. This paper introduces the k-test to measure the approximation hardness of inference on Bayesian networks with deterministic causalities in the probability distribution, i.e. when zero conditional probabilities are permitted. Approximation by stochastic sampling is a widely-used inference method that is known to suffer from inefficiencies due to sample rejection. The k-test predicts when rejection rates of stochastic sampling a Bayesian network will be low, modest, high, or when sampling is intractable.

We introduce a rich class of graphical models for multi-armed bandit problems that permit both the state or context space and the action space to be very large, yet succinctly specify the payoffs for any context-action pair. Our main result is an algorithm for such models whose regret is bounded by the number of parameters and whose running time depends only on the treewidth of the graph substructure induced by the action space.