scholarly journals Iterative Planning for Deterministic QDec-POMDPs

10.29007/4t8s ◽  
2018 ◽  
Author(s):  
Sagi Bazinin ◽  
Guy Shani
Keyword(s):  
Scale Up ◽  
Action Execution ◽  
Worst Case ◽  
State Spaces ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Distributed Execution ◽  
Multi Agent ◽  
Partially Observable ◽  
Joint Plan

QDec-POMDPs are a qualitative alternative to stochastic Dec-POMDPs for goal-oriented plan- ning in cooperative partially observable multi-agent environments. Although QDec-POMDPs share the same worst case complexity as Dec-POMDPs, previous research has shown an ability to scale up to larger domains while producing high quality plan trees. A key difficulty in distributed execution is the need to construct a joint plan tree branching on the combinations of observations of all agents. In this work, we suggest an iterative algorithm, IMAP, that plans for one agent at a time, taking into considerations collaboration constraints about action execution of previous agents, and generating new constraints for the next agents. We explain how these constraints are generated and handled, and a backtracking mechanism for changing constraints that cannot be met. We provide experimental results on multi-agent planning domains, showing our methods to scale to much larger problems with several collaborating agents and huge state spaces.

scholarly journals Some Things are Easier for the Dumb and the Bright Ones (Beware the Average!)

2019 ◽  
Author(s):  
Wojciech Jamroga ◽  
Michał Knapik
Keyword(s):  
Model Checking ◽  
Multi Agent Systems ◽  
Worst Case ◽  
Case Complexity ◽  
Special Cases ◽  
Worst Case Complexity ◽  
Multi Agent ◽  
Np Complete ◽  
Epistemic Structure ◽  
Verification Of Models

Model checking strategic abilities in multi-agent systems is hard, especially for agents with partial observability of the state of the system. In that case, it ranges from NP-complete to undecidable, depending on the precise syntax and the semantic variant. That, however, is the worst case complexity, and the problem might as well be easier when restricted to particular subclasses of inputs. In this paper, we look at the verification of models with "extreme" epistemic structure, and identify several special cases for which model checking is easier than in general. We also prove that, in the other cases, no gain is possible even if the agents have almost full (or almost nil) observability. To prove the latter kind of results, we develop generic techniques that may be useful also outside of this study.

scholarly journals On the optimal order of worst case complexity of direct search

2015 ◽  
Vol 10 (4) ◽  
pp. 699-708 ◽  
Author(s):  
M. Dodangeh ◽  
L. N. Vicente ◽  
Z. Zhang
Keyword(s):  
Direct Search ◽  
Optimal Order ◽  
Worst Case ◽  
Case Complexity ◽  
Worst Case Complexity

Worst-case Complexity of Exact Algorithms forNP-hard Problems

2010 ◽  
pp. 203-240
Author(s):  
Federico Della Croce ◽  
Bruno Escoffier ◽  
Marcin Kamiski ◽  
Vangelis Th. Paschos
Keyword(s):  
Exact Algorithms ◽  
Worst Case ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Hard Problems

scholarly journals Logic-based specification and verification of homogeneous dynamic multi-agent systems

2020 ◽  
Vol 34 (2) ◽  
Author(s):  
Riccardo De Masellis ◽  
Valentin Goranko
Keyword(s):  
Normal Form ◽  
Model Checking ◽  
Formal Specification ◽  
Formal Semantics ◽  
Fixed Number ◽  
State Transitions ◽  
Multi Agent Systems ◽  
Worst Case ◽  
Worst Case Complexity ◽  
Multi Agent

Abstract We develop a logic-based framework for formal specification and algorithmic verification of homogeneous and dynamic concurrent multi-agent transition systems. Homogeneity means that all agents have the same available actions at any given state and the actions have the same effects regardless of which agents perform them. The state transitions are therefore determined only by the vector of numbers of agents performing each action and are specified symbolically, by means of conditions on these numbers definable in Presburger arithmetic. The agents are divided into controllable (by the system supervisor/controller) and uncontrollable, representing the environment or adversary. Dynamicity means that the numbers of controllable and uncontrollable agents may vary throughout the system evolution, possibly at every transition. As a language for formal specification we use a suitably extended version of Alternating-time Temporal Logic, where one can specify properties of the type “a coalition of (at least) n controllable agents can ensure against (at most) m uncontrollable agents that any possible evolution of the system satisfies a given objective $$\gamma$$ γ ″, where $$\gamma$$ γ is specified again as a formula of that language and each of n and m is either a fixed number or a variable that can be quantified over. We provide formal semantics to our logic $${\mathcal {L}}_{\textsc {hdmas}}$$ L H D M A S and define normal form of its formulae. We then prove that every formula in $${\mathcal {L}}_{\textsc {hdmas}}$$ L H D M A S is equivalent in the finite to one in a normal form and develop an algorithm for global model checking of formulae in normal form in finite HDMAS models, which invokes model checking truth of Presburger formulae. We establish worst case complexity estimates for the model checking algorithm and illustrate it on a running example.

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