Markov processes are increasingly used to generate finite-length sequences that imitate a given style. However, Markov processes are notoriously difficult to control. Recently, Markov constraints have been introduced to give users some control on generated sequences. Markov constraints reformulate finite-length Markov sequence generation in the framework of constraint satisfaction (CSP). However, in practice, this approach is limited to local constraints and its performance is low for global constraints, such as cardinality or arithmetic constraints. This limitation prevents generated sequences to follow structural properties which are independent of the style, but inherent to the domain, such as meter. In this article, we introduce meter, a constraint that ensures a sequence is 1) Markovian with regards to a given corpus and 2) follows metrical rules expressed as cumulative cost functions. Additionally, meter can simultaneously enforce cardinality constraints. We propose a domain consistency algorithm whose complexity is pseudo-polynomial. This result is obtained thanks to a theorem on the growth of sumsets by Khovanskii. We illustrate our constraint on meter-constrained music generation problems that were so far not solvable by any other technique.

Social choice theory provides insights into a variety of collective decision making settings, but nowadays some of its tenets are challenged by internet environments, which call for dynamic decision making under constantly changing preferences. In this paper we model the problem via Markov decision processes (MDP), where the states of the MDP coincide with preference profiles and a (deterministic, stationary) policy corresponds to a social choice function. We can therefore employ the axioms studied in the social choice literature as guidelines in the design of socially desirable policies. We present tractable algorithms that compute optimal policies under different prominent social choice constraints. Our machinery relies on techniques for exploiting symmetries and isomorphisms between MDPs.

The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to outperform standard estimators by several orders of magnitude. The developed theory and algorithms apply to a broad class of probabilistic models including statistical relational models considered not susceptible to lifted probabilistic inference.

Learning accurate models of agent behaviours is crucial for the purpose of controlling systems where the agents' and environment's dynamics are unknown. This is a challenging problem, but structural assumptions can be leveraged to tackle it effectively. In particular, many systems exhibit mixed observability, when observations of some system components are essentially perfect and noiseless, while observations of other components are imperfect, aliased or noisy. In this paper we present a new model learning framework, the mixed observability predictive state representation (MO-PSR), which extends the previously known predictive state representations to the case of mixed observability systems. We present a learning algorithm that is scalable to large amounts of data and to large mixed observability domains, and show theoretical analysis of the learning consistency and computational complexity. Empirical results demonstrate that our algorithm is capable of learning accurate models, at a larger scale than with the generic predictive state representation, by leveraging the mixed observability properties.

By handling whole sets of indistinguishable objects together, lifted belief propagation approaches have rendered large, previously intractable, probabilistic inference problems quickly solvable. In this paper, we show that Kumar and Zilberstein's likelihood maximization (LM) approach to MAP inference is liftable, too, and actually provides additional structure for optimization. Specifically, it has been recognized that some pseudo marginals may converge quickly, turning intuitively into pseudo evidence. This additional evidence typically changes the structure of the lifted network: it may expand or reduce it. The current lifted network, however, can be viewed as an upper bound on the size of the lifted network required to finish likelihood maximization. Consequently, we re-lift the network only if the pseudo evidence yields a reduced network, which can efficiently be computed on the current lifted network. Our experimental results on Ising models, image segmentation and relational entity resolution demonstrate that this bootstrapped LM via "reduce and re-lift" finds MAP assignments comparable to those found by the original LM approach, but in a fraction of the time.

Decentralized POMDPs (Dec-POMDPs) provide a rich, attractive model for planning under uncertainty and partial observability in cooperative multi-agent domains with a growing body of research. In this paper we formulate a qualitative, propositional model for multi-agent planning under uncertainty with partial observability, which we call Qualitative Dec-POMDP (QDec-POMDP). We show that the worst-case complexity of planning in QDec-POMDPs is similar to that of Dec-POMDPs. Still, because the model is more “classical” in nature, it is more compact and easier to specify. Furthermore, it eases the adaptation of methods used in classical and contingent planning to solve problems that challenge current Dec-POMDPs solvers. In particular, in this paper we describe a method based on compilation to classical planning, which handles multi-agent planning problems significantly larger than those handled by current Dec-POMDP algorithms.

RockIt is a maximum a-posteriori (MAP) query engine for statistical relational models. MAP inference in graphical models is an optimization problem which can be compiled to integer linear programs (ILPs).We describe several advances in translating MAP queries to ILP instances and present the novel meta-algorithm cutting plane aggregation (CPA). CPA exploits local context-specific symmetries and bundles up sets of linear constraints. The resulting counting constraints lead to more compact ILPs and make the symmetry of the ground model more explicit to state-of-the-art ILP solvers. Moreover, RockIt parallelizes most parts of the MAP inference pipeline taking advantage of ubiquitous shared-memory multi-core architectures. We report on extensive experiments with Markov logic network (MLN) benchmarks showing that RockIt outperforms the state-of-the-art systems Alchemy, Markov TheBeast, and Tuffy both in terms of efficiency and quality of results.

This paper tackles high-level decision-making techniques for robotic missions, which involve both active sensing and symbolic goal reaching, under uncertain probabilistic environments and strong time constraints. Our case study is a POMDP model of an online multi-target detection and recognition mission by an autonomous UAV. The POMDP model of the multi-target detection and recognition problem is generated online from a list of areas of interest, which are automatically extracted at the beginning of the flight from a coarse-grained high altitude observation of the scene. The POMDP observation model relies on a statistical abstraction of an image processing algorithm's output used to detect targets. As the POMDP problem cannot be known and thus optimized before the beginning of the flight, our main contribution is an "optimize-while-execute" algorithmic framework: it drives a POMDP sub-planner to optimize and execute the POMDP policy in parallel under action duration constraints. We present new results from real outdoor flights and SAIL simulations, which highlight both the benefits of using POMDPs in multi-target detection and recognition missions, and of our "optimize-while-execute" paradigm.

Decentralized partially observable Markov decision processes (Dec-POMDPs) offer a powerful modeling technique for realistic multi-agent coordination problems under uncertainty. Prevalent solution techniques are centralized and assume prior knowledge of the model. Recently a Monte Carlo based distributed reinforcement learning approach was proposed, where agents take turns to learn best responses to each other’s policies. This promotes decentralization of the policy computation problem, and relaxes reliance on the full knowledge of the problem parameters. However, this Monte Carlo approach has a large sample complexity, which we address in this paper. In particular, we propose and analyze a modified version of the previous algorithm that adaptively eliminates parts of the experience tree from further exploration, thus requiring fewer samples while ensuring unchanged confidence in the learned value function. Experiments demonstrate significant reduction in sample complexity – the maximum reductions ranging from 61% to 91% over different benchmark Dec-POMDP problems – with the final policies being often better due to more focused exploration.

Current exploration algorithms can be classified in two broad categories: Heuristic, and PAC optimal. While numerous researchers have used heuristic approaches such as epsilon-greedy exploration successfully, such approaches lack formal, finite sample guarantees and may need a significant amount of fine-tuning to produce good results. PAC optimal exploration algorithms, on the other hand, offer strong theoretical guarantees but are inapplicable in domains of realistic size. The goal of this paper is to bridge the gap between theory and practice, by introducing C-PACE, an algorithm which offers strong theoretical guarantees and can be applied to interesting, continuous space problems.