180 research outputs found
Mixed Integer Linear Programming For Exact Finite-Horizon Planning In Decentralized Pomdps
We consider the problem of finding an n-agent joint-policy for the optimal
finite-horizon control of a decentralized Pomdp (Dec-Pomdp). This is a problem
of very high complexity (NEXP-hard in n >= 2). In this paper, we propose a new
mathematical programming approach for the problem. Our approach is based on two
ideas: First, we represent each agent's policy in the sequence-form and not in
the tree-form, thereby obtaining a very compact representation of the set of
joint-policies. Second, using this compact representation, we solve this
problem as an instance of combinatorial optimization for which we formulate a
mixed integer linear program (MILP). The optimal solution of the MILP directly
yields an optimal joint-policy for the Dec-Pomdp. Computational experience
shows that formulating and solving the MILP requires significantly less time to
solve benchmark Dec-Pomdp problems than existing algorithms. For example, the
multi-agent tiger problem for horizon 4 is solved in 72 secs with the MILP
whereas existing algorithms require several hours to solve it
Planning for Decentralized Control of Multiple Robots Under Uncertainty
We describe a probabilistic framework for synthesizing control policies for
general multi-robot systems, given environment and sensor models and a cost
function. Decentralized, partially observable Markov decision processes
(Dec-POMDPs) are a general model of decision processes where a team of agents
must cooperate to optimize some objective (specified by a shared reward or cost
function) in the presence of uncertainty, but where communication limitations
mean that the agents cannot share their state, so execution must proceed in a
decentralized fashion. While Dec-POMDPs are typically intractable to solve for
real-world problems, recent research on the use of macro-actions in Dec-POMDPs
has significantly increased the size of problem that can be practically solved
as a Dec-POMDP. We describe this general model, and show how, in contrast to
most existing methods that are specialized to a particular problem class, it
can synthesize control policies that use whatever opportunities for
coordination are present in the problem, while balancing off uncertainty in
outcomes, sensor information, and information about other agents. We use three
variations on a warehouse task to show that a single planner of this type can
generate cooperative behavior using task allocation, direct communication, and
signaling, as appropriate
Stochastic Shortest Path with Energy Constraints in POMDPs
We consider partially observable Markov decision processes (POMDPs) with a
set of target states and positive integer costs associated with every
transition. The traditional optimization objective (stochastic shortest path)
asks to minimize the expected total cost until the target set is reached. We
extend the traditional framework of POMDPs to model energy consumption, which
represents a hard constraint. The energy levels may increase and decrease with
transitions, and the hard constraint requires that the energy level must remain
positive in all steps till the target is reached. First, we present a novel
algorithm for solving POMDPs with energy levels, developing on existing POMDP
solvers and using RTDP as its main method. Our second contribution is related
to policy representation. For larger POMDP instances the policies computed by
existing solvers are too large to be understandable. We present an automated
procedure based on machine learning techniques that automatically extracts
important decisions of the policy allowing us to compute succinct human
readable policies. Finally, we show experimentally that our algorithm performs
well and computes succinct policies on a number of POMDP instances from the
literature that were naturally enhanced with energy levels.Comment: Technical report accompanying a paper published in proceedings of
AAMAS 201
Multiagent Planning and Learning As MILP
National audienceThe decentralized partially observable Markov decisionprocess offers a unified framework for sequential decision-making by multiple collaborating agents but remains in-tractable. Mixed-integer linear formulations proved use-ful for partially observable domains, unfortunately ex-isting applications restrict to domains with one or twoagents. In this paper, we exploit a linearization propertythat allows us to reformulate nonlinear constraints fromn-agent settings into linear ones. We further present plan-ning and learning approaches relying on MILP formula-tions for general and special cases, including network-distributed and transition-independent problems. Experi-ments on standard2-agent benchmarks as well as domainswith a large number of agents provide strong empiricalsupport to the methodology.Les processus décisionnels de Markov décentralises et partiellement observables (Dec-POMDPs) offrent un cadre unifie pour la prise de décisions séquentielles par de plusieurs agents collaboratifs—mais ils restent difficiles`a résoudre. Les reformulations en programmes linéaires mixtes (PLMs) se sont avérées utiles pour les processus décisionnels de Markov partiellement observables.Malheureusement, les applications existantes se limitent uniquement aux domaines mobilisant un ou deux agents. Dans cet article, nous exploitons une propriété de linéarisation qui nous permet de reformuler les contraintes non linéaires, omniprésentes dans les systèmes multi-agents, pour en faire des contraintes linéaires. Nous présentons en outre des approches de planification et d’apprentissage s’appuyant sur de nouvelles reformulations en PLMs des Dec-POMDPs, dans le cas général ainsi que quelques cas spécifiques. Les expérimentations sur des bancs de test standards`a deux et plus de deux agents fournissent un solide soutien`a cette méthodologie
Optimal and Approximate Q-value Functions for Decentralized POMDPs
Decision-theoretic planning is a popular approach to sequential decision
making problems, because it treats uncertainty in sensing and acting in a
principled way. In single-agent frameworks like MDPs and POMDPs, planning can
be carried out by resorting to Q-value functions: an optimal Q-value function
Q* is computed in a recursive manner by dynamic programming, and then an
optimal policy is extracted from Q*. In this paper we study whether similar
Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs),
and how policies can be extracted from such value functions. We define two
forms of the optimal Q-value function for Dec-POMDPs: one that gives a
normative description as the Q-value function of an optimal pure joint policy
and another one that is sequentially rational and thus gives a recipe for
computation. This computation, however, is infeasible for all but the smallest
problems. Therefore, we analyze various approximate Q-value functions that
allow for efficient computation. We describe how they relate, and we prove that
they all provide an upper bound to the optimal Q-value function Q*. Finally,
unifying some previous approaches for solving Dec-POMDPs, we describe a family
of algorithms for extracting policies from such Q-value functions, and perform
an experimental evaluation on existing test problems, including a new
firefighting benchmark problem
Apprendre Ă agir dans un Dec-POMDP
We address a long-standing open problem of reinforcement learning in decentralized partiallyobservable Markov decision processes. Previous attempts focussed on different forms of generalized policyiteration, which at best led to local optima. In this paper, we restrict attention to plans, which are simplerto store and update than policies. We derive, under certain conditions, the first near-optimal cooperativemulti-agent reinforcement learning algorithm. To achieve significant scalability gains, we replace the greedymaximization by mixed-integer linear programming. Experiments show our approach can learn to actnear-optimally in many finite domains from the literature
Learning to Act in Decentralized Partially Observable MDPs
International audienceWe address a long-standing open problem of reinforcement learning in decentralized partially observable Markov decision processes. Previous attempts focussed on different forms of generalized policy iteration, which at best led to local optima. In this paper, we restrict attention to plans, which are simpler to store and update than policies. We derive, under certain conditions, the first near-optimal cooperative multi-agent reinforcement learning algorithm. To achieve significant scalability gains, we replace the greedy maximization by mixed-integer linear programming. Experiments show our approach can learn to act near-optimally in many finite domains from the literature
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