223 research outputs found
Approximating n-player behavioural strategy nash equilibria using coevolution
Coevolutionary algorithms are plagued with a set of problems related to intransitivity that make it questionable what the end product of a coevolutionary run can achieve. With the introduction of solution concepts into coevolution, part of the issue was alleviated, however efficiently representing and achieving game theoretic solution concepts is still not a trivial task. In this paper we propose a coevolutionary algorithm that approximates behavioural strategy Nash equilibria in n-player zero sum games, by exploiting the minimax solution concept. In order to support our case we provide a set of experiments in both games of known and unknown equilibria. In the case of known equilibria, we can confirm our algorithm converges to the known solution, while in the case of unknown equilibria we can see a steady progress towards Nash. Copyright 2011 ACM
A Parallel Monte-Carlo Tree Search-Based Metaheuristic For Optimal Fleet Composition Considering Vehicle Routing Using Branch & Bound
In this paper, a Monte-Carlo Tree Search (MCTS)-based metaheuristic is
developed that guides a Branch & Bound (B&B) algorithm to find the globally
optimal solution to the heterogeneous fleet composition problem while
considering vehicle routing. Fleet Size and Mix Vehicle Routing Problem with
Time Windows (FSMVRPTW). The metaheuristic and exact algorithms are implemented
in a parallel hybrid optimization algorithm where the metaheuristic rapidly
finds feasible solutions that provide candidate upper bounds for the B&B
algorithm which runs simultaneously. The MCTS additionally provides a candidate
fleet composition to initiate the B&B search. Experiments show that the
proposed approach results in significant improvements in computation time and
convergence to the optimal solution.Comment: Submitted to the IEEE Intelligent Vehicles Symposium 202
Bootstrapping Monte Carlo Tree Search with an Imperfect Heuristic
We consider the problem of using a heuristic policy to improve the value
approximation by the Upper Confidence Bound applied in Trees (UCT) algorithm in
non-adversarial settings such as planning with large-state space Markov
Decision Processes. Current improvements to UCT focus on either changing the
action selection formula at the internal nodes or the rollout policy at the
leaf nodes of the search tree. In this work, we propose to add an auxiliary arm
to each of the internal nodes, and always use the heuristic policy to roll out
simulations at the auxiliary arms. The method aims to get fast convergence to
optimal values at states where the heuristic policy is optimal, while retaining
similar approximation as the original UCT in other states. We show that
bootstrapping with the proposed method in the new algorithm, UCT-Aux, performs
better compared to the original UCT algorithm and its variants in two benchmark
experiment settings. We also examine conditions under which UCT-Aux works well.Comment: 16 pages, accepted for presentation at ECML'1
Anytime Algorithms for Solving Possibilistic MDPs and Hybrid MDPs
The ability of an agent to make quick, rational decisions in an uncertain environment is paramount for its applicability in realistic settings. Markov Decision Processes (MDP) provide such a framework, but can only model uncertainty that can be expressed as probabilities. Possibilistic counterparts of MDPs allow to model imprecise beliefs, yet they cannot accurately represent probabilistic sources of uncertainty and they lack the efficient online solvers found in the probabilistic MDP community. In this paper we advance the state of the art in three important ways. Firstly, we propose the first online planner for possibilistic MDP by adapting the Monte-Carlo Tree Search (MCTS) algorithm. A key component is the development of efficient search structures to sample possibility distributions based on the DPY transformation as introduced by Dubois, Prade, and Yager. Secondly, we introduce a hybrid MDP model that allows us to express both possibilistic and probabilistic uncertainty, where the hybrid model is a proper extension of both probabilistic and possibilistic MDPs. Thirdly, we demonstrate that MCTS algorithms can readily be applied to solve such hybrid models. © Springer International Publishing Switzerland 2016.This work is partially funded by EPSRC PACES project (Ref: EP/J012149/1).Peer Reviewe
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