Optimal Factory Scheduling using Stochastic Dominance A*

We examine a standard factory scheduling problem with stochastic processing and setup times, minimizing the expectation of the weighted number of tardy jobs. Because the costs of operators in the schedule are stochastic and sequence dependent, standard dynamic programming algorithms such as A* may fail to find the optimal schedule. The SDA* (Stochastic Dominance A*) algorithm remedies this difficulty by relaxing the pruning condition. We present an improved state-space search formulation for these problems and discuss the conditions under which stochastic scheduling problems can be solved optimally using SDA*. In empirical testing on randomly generated problems, we found that in 70%, the expected cost of the optimal stochastic solution is lower than that of the solution derived using a deterministic approximation, with comparable search effort.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Incremental Tradeoff Resolution in Qualitative Probabilistic Networks

Qualitative probabilistic reasoning in a Bayesian network often reveals tradeoffs: relationships that are ambiguous due to competing qualitative influences. We present two techniques that combine qualitative and numeric probabilistic reasoning to resolve such tradeoffs, inferring the qualitative relationship between nodes in a Bayesian network. The first approach incrementally marginalizes nodes that contribute to the ambiguous qualitative relationships. The second approach evaluates approximate Bayesian networks for bounds of probability distributions, and uses these bounds to determinate qualitative relationships in question. This approach is also incremental in that the algorithm refines the state spaces of random variables for tighter bounds until the qualitative relationships are resolved. Both approaches provide systematic methods for tradeoff resolution at potentially lower computational cost than application of purely numeric methods.Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998

Graphical Representations of Consensus Belief

Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We prove, under relatively mild assumptions, that even if everyone agrees on a common graph topology, no method of combining beliefs can maintain that structure. Even weaker conditions rule out local aggregation within conditional probability tables. On a more positive note, we show that if probabilities are combined with the logarithmic opinion pool (LogOP), then commonly held Markov independencies are maintained. This suggests a straightforward procedure for constructing a consensus Markov network. We describe an algorithm for computing the LogOP with time complexity comparable to that of exact Bayesian inference.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Toward a Market Model for Bayesian Inference

We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and producers trade in uncertain propositions. We demonstrate the correspondence between the equilibrium prices of goods in this economy and the probabilities represented by the Bayesian network. A computational market model such as this may provide a useful framework for investigations of belief aggregation, distributed probabilistic inference, resource allocation under uncertainty, and other problems of decentralized uncertainty.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

State-space Abstraction for Anytime Evaluation of Probabilistic Networks

One important factor determining the computational complexity of evaluating a probabilistic network is the cardinality of the state spaces of the nodes. By varying the granularity of the state spaces, one can trade off accuracy in the result for computational efficiency. We present an anytime procedure for approximate evaluation of probabilistic networks based on this idea. On application to some simple networks, the procedure exhibits a smooth improvement in approximation quality as computation time increases. This suggests that state-space abstraction is one more useful control parameter for designing real-time probabilistic reasoners.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Probabilistic State-Dependent Grammars for Plan Recognition

Techniques for plan recognition under uncertainty require a stochastic model of the plan-generation process. We introduce Probabilistic State-Dependent Grammars (PSDGs) to represent an agent's plan-generation process. The PSDG language model extends probabilistic context-free grammars (PCFGs) by allowing production probabilities to depend on an explicit model of the planning agent's internal and external state. Given a PSDG description of the plan-generation process, we can then use inference algorithms that exploit the particular independence properties of the PSDG language to efficiently answer plan-recognition queries. The combination of the PSDG language model and inference algorithms extends the range of plan-recognition domains for which practical probabilistic inference is possible, as illustrated by applications in traffic monitoring and air combat.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

Accounting for Context in Plan Recognition, with Application to Traffic Monitoring

Typical approaches to plan recognition start from a representation of an agent's possible plans, and reason evidentially from observations of the agent's actions to assess the plausibility of the various candidates. A more expansive view of the task (consistent with some prior work) accounts for the context in which the plan was generated, the mental state and planning process of the agent, and consequences of the agent's actions in the world. We present a general Bayesian framework encompassing this view, and focus on how context can be exploited in plan recognition. We demonstrate the approach on a problem in traffic monitoring, where the objective is to induce the plan of the driver from observation of vehicle movements. Starting from a model of how the driver generates plans, we show how the highway context can appropriately influence the recognizer's interpretation of observed driver behavior.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Self-Confirming Price Prediction Strategies for Simultaneous One-Shot Auctions

Bidding in simultaneous auctions is challenging because an agent's value for a good in one auction may depend on the uncertain outcome of other auctions: the so-called exposure problem. Given the gap in understanding of general simultaneous auction games, previous works have tackled this problem with heuristic strategies that employ probabilistic price predictions. We define a concept of self-confirming prices, and show that within an independent private value model, Bayes-Nash equilibrium can be fully characterized as a profile of optimal price prediction strategies with self-confirming predictions. We exhibit practical procedures to compute approximately optimal bids given a probabilistic price prediction, and near self-confirming price predictions given a price-prediction strategy. An extensive empirical game-theoretic analysis demonstrates that self-confirming price prediction strategies are effective in simultaneous auction games with both complementary and substitutable preference structures.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

Path Planning under Time-Dependent Uncertainty

Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential probabilistic dependencies among the costs. Although these dependencies violate the standard dynamic-programming decomposition, we identify a weaker stochastic consistency condition that justifies a generalized dynamic-programming approach based on stochastic dominance. We present a revised path-planning algorithm and prove that it produces optimal paths under time-dependent uncertain costs. We test the algorithm by applying it to a model of stochastic bus networks, and present empirical performance results comparing it to some alternatives. Finally, we consider extensions of these concepts to a more general class of problems of heuristic search under uncertainty.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Knowledge Combination in Graphical Multiagent Model

A graphical multiagent model (GMM) represents a joint distribution over the behavior of a set of agents. One source of knowledge about agents' behavior may come from gametheoretic analysis, as captured by several graphical game representations developed in recent years. GMMs generalize this approach to express arbitrary distributions, based on game descriptions or other sources of knowledge bearing on beliefs about agent behavior. To illustrate the flexibility of GMMs, we exhibit game-derived models that allow probabilistic deviation from equilibrium, as well as models based on heuristic action choice. We investigate three different methods of integrating these models into a single model representing the combined knowledge sources. To evaluate the predictive performance of the combined model, we treat as actual outcome the behavior produced by a reinforcement learning process. We find that combining the two knowledge sources, using any of the methods, provides better predictions than either source alone. Among the combination methods, mixing data outperforms the opinion pool and direct update methods investigated in this empirical trial.Comment: Appears in Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence (UAI2008