Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to represent the local policy of each agent. These variable-size FSCs are constructed using a stick-breaking prior, leading to a new framework called (Dec-SBPR). This approach learns the controller parameters with a variational Bayesian algorithm without having to assume that the Dec-POMDP model is available. The performance of Dec-SBPR is demonstrated on several benchmark problems, showing that the algorithm scales to large problems while outperforming other state-of-the-art methods.
The proof of Theorem in the single-agent case ( @math ) has been given in @cite_14 that the empirical value function ). Proof for @math is similar and is omitted here.
@cite_14
2041385195 2062285040 1931447968 1540024383
We consider the problem of allocating some amount of a commodity among a group of agents with single-peaked preferences. We show that the uniform rule is the only rule satisfying equal treatment of equals, Pareto efficiency, and strategy-proofness. This characterization strengthens two interesting results due to Sprumont (1991). Our method of proof involves only elementary arguments. We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say «according to agent i, formula φ holds with probability at least b.» The language is powerful enough to allow reasoning about higher-order probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, and consider various properties that might hold of the interrelationship between agents' probability assignments at different states. We provide a complete axiomatization for reasoning about knowledge and probability, prove a small model property, and obtain decision procedures For more than three and one-half decades, beginning in the early 1960s, a heavy emphasis on proof finding has been a key component of the Argonne paradigm, whose use has directly led to significant advances in automated reasoning and important contributions to mathematics and logic. The theorems studied range from the trivial to the deep, even including some that corresponded to open questions. Often the paradigm asks for a theorem whose proof is in hand but that cannot be obtained in a fully automated manner by the program in use. The theorem whose hypothesis consists solely of the Meredith single axiom for two-valued sentential (or propositional) calculus and whose conclusion is the Lukasiewicz three-axiom system for that area of formal logic was just such a theorem. Featured in this article is the methodology that enabled the program OTTER to find the first fully automated proof of the cited theorem, a proof with the intriguing property that none of its steps contains a term of the form i>n(i>n(i>t)) for any term i>t. As evidence of the power of the new methodology, the article also discusses OTTER's success in obtaining the first known proof of a theorem concerning a single axiom of Lukasiewicz. In this paper we present an extension of logic programming (LP) that is suitable not only for the “rational” component of a single agent but also for the “reactive” component and that can encompass multidagent systems. We modify an earlier abductive proof procedure and embed it within an agent cycle. The proof procedure incorporates abduction, definitions and integrity constraints within a dynamic environment, where changes can be observed as inputs. The definitions allow rational planning behaviour and the integrity constraints allow reactive, conditiondaction type behaviour. The agent cycle provides a resourcedbounded mechanism that allows the agent’s thinking to be interrupted for the agent to record and assimilate observations as input and execute actions as output, before resuming further thinking. We argue that these extensions of LP, accommodating multidtheories embedded in a shared environment, provide the necessary multidagent functionality. We argue also that our work extends Shoham’s Agent0 and the BDI architecture.