Aggregate factors (that is, those based on aggregate functions such as SUM, AVERAGE, AND etc.) in probabilistic relational models can compactly represent dependencies among a large number of relational random variables. However, propositional inference on a factor aggregating n k -valued random variables into an r -valued result random variable is O ( r k 2 n ). Lifted methods can ameliorate this to O ( r n k ) in general and O ( r k log n ) for commutative associative aggregators. In this paper, we propose (a) an exact solution constant in n when k  = 2 for certain aggregate operations such as AND, OR and SUM, and (b) a close approximation for inference with aggregate factors with time complexity constant in n . This approximate inference involves an analytical solution for some operations when k > 2. The approximation is based on the fact that the typically used aggregate functions can be represented by linear constraints in the standard ( k  –1)-simplex in R k where k is the number of possible values for random variables. This includes even aggregate functions that are commutative but not associative (e.g., the MODE operator that chooses the most frequent value). Our algorithm takes polynomial time in k (which is only 2 for binary variables) regardless of r and n, and the error decreases as n increases. Therefore, for most applications (in which a close approximation suffices) our algorithm is a much more efficient solution than existing algorithms. We present experimental results supporting these claims. We also present a (c) third contribution which further optimizes aggregations over multiple groups of random variables with distinct distributions.

Students have implemented approaches to these problems, using our HRTeam framework (Sklar et al. 2010), which is built on Player/Stage (Vaughan and Gerkey 2007).

We describe a robot system that autonomously acquires skills through interaction with its environment. The robot learns to sequence the execution of a set of innate controllers to solve a task, extracts and retains components of that solution as portable skills, and then transfers those skills to reduce the time required to learn to solve a second task.

In this work we present an advanced Bayesian formulation to the task of control learning that employs the Relevance Vector Machines (RVM) generative model for value function evaluation. The key aspect of the proposed method is the design of the discount return as a generalized linear model that constitutes a well-known probabilistic approach. This allows to augment the model with advantageous sparse priors provided by the RVM's regression framework. We have also taken into account the significant issue of selecting the proper parameters of the kernel design matrix. Experiments have shown that our method produces improved performance in both simulated and real test environments.

One proposed approach to managing a large complex Smart Grid is through Broker Agents who buy electrical power from distributed producers, and also sell power to consumers, via a Tariff Market--a new market mechanism where Broker Agents publish concurrent bid and ask prices. A key challenge is the specification of the market strategy that the Broker Agents should use in order to earn profits while maintaining the market's balance of supply and demand. Interestingly, previous work has shown that a Broker Agent can learn its strategy, using Markov Decision Processes (MDPs) and Q-learning, and outperform other Broker Agents that use predetermined or randomized strategies. In this work, we investigate the more representative scenario in which multiple Broker Agents, instead of a single one, are independently learning their strategies. Using a simulation environment based on real data, we find that Broker Agents who employ periodic increases in exploration achieve higher rewards. We also find that varying levels of market dominance in customer allocation models result in remarkably distinct outcomes in market prices and aggregate Broker Agent rewards. The latter set of results can be explained by established economic principles regarding the emergence of monopolies in market-based competition, further validating our approach.

This paper extends existing plan recognition research to handle plans containing loops. We supply an encoding of plans with loops for recognition, based on techniques used to parse lexicalized grammars, and demonstrate its effectiveness empirically. To do this, the paper first shows how encoding plan libraries as context free grammars permits the application of standard rewriting techniques to remove left recursion and ε-productions, thereby enabling polynomial time parsing. However, these techniques alone fail to provide efficient algorithms for plan recognition. We show how the loop-handling methods from formal grammars can be extended to the more general plan recognition problem and provide a method for encoding loops in an existing plan recognition system that scales linearly in the number of loop iterations.

We consider settings in which a semi-autonomous agent has uncertain knowledge about its environment, but can ask what action the human operator would prefer taking in the current or in a potential future state. Asking queries can improve behavior, but if queries come at a cost (e.g., due to limited operator attention), the value of each query should be maximized. We compare two strategies for selecting action queries: 1) based on myopically maximizing expected gain in long-term value, and 2) based on myopically minimizing uncertainty in the agent's policy representation. We show empirically that the first strategy tends to select more valuable queries, and that a hybrid method can outperform either method alone in settings with limited computation.

The conservation of wildlife corridors between existing habitat preserves is important for combating the effects of habitat loss and fragmentation facing species of concern. We introduce the Steiner Multigraph Problem to model the problem of minimum-cost wildlife corridor design for multiple species with different landscape requirements. This problem can also model other analogous settings in wireless and social networks. As a generalization of Steiner forest, the goal is to find a minimum-cost subgraph that connects multiple sets of terminals. In contrast to Steiner forest, each set of terminals can only be connected via a subset of the nodes. Generalizing Steiner forest in this way makes the problem NP-hard even when restricted to two pairs of terminals. However, we show that if the node subsets have a nested structure, the problem admits a fixed-parameter tractable algorithm in the number of terminals. We successfully test exact and heuristic solution approaches on a wildlife corridor instance for wolverines and lynx in western Montana, showing that though the problem is computationally hard, heuristics perform well, and provably optimal solutions can still be obtained.

MAPP has been previously shown as a state-of-the-art multi-agent path planning algorithm on criteria including scalability and success ratio (i.e., percentage of solved units) on realistic game maps. MAPP further provides a formal characterization of problems it can solve, and low-polynomial upper bounds on the resources required. However, until now, MAPP's solution quality had not been extensively analyzed. In this work we empirically analyze the quality of MAPP's solutions, using multiple quality criteria such as the total travel distance, the makespan and the sum of actions (including move and wait actions). We also introduce enhancements that improve MAPP's solution quality significantly. For example, the sum of actions is cut to half on average. The improved MAPP is competitive in terms of solution quality with FAR and WHCA*, two successful algorithms from the literature, and maintains its advantages on different performance criteria, such as scalability, success ratio, and ability to tell apriori if it will succeed in the instance at hand. As optimal algorithms have limited scalability, evaluating the quality of the solutions provided by suboptimal algorithms is another important topic. Using lower bounds of optimal values, we show that MAPP's solutions have a reasonable quality. For example, MAPP's total travel distance is on average 19% longer than a lower bound on the optimal value.

Sustainable resource management in many domains presents large continuous stochastic optimization problems, which can often be modeled as Markov decision processes (MDPs). To solve such large MDPs, we identify and leverage linearity in state and action sets that is common in resource management. In particular, we introduce linear dynamic programs (LDPs) that generalize resource management problems and partially observable MDPs (POMDPs). We show that the LDP framework makes it possible to adapt point-based methods--the state of the art in solving POMDPs--to solving LDPs. The experimental results demonstrate the efficiency of this approach in managing the water level of a river reservoir. Finally, we discuss the relationship with dual dynamic programming, a method used to optimize hydroelectric systems.