4 research outputs found
Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes
In this paper, we consider algorithms to decide the existence of strategies
in MDPs for Boolean combinations of objectives. These objectives are
omega-regular properties that need to be enforced either surely, almost surely,
existentially, or with non-zero probability. In this setting, relevant
strategies are randomized infinite memory strategies: both infinite memory and
randomization may be needed to play optimally. We provide algorithms to solve
the general case of Boolean combinations and we also investigate relevant
subcases. We further report on complexity bounds for these problems.Comment: Paper accepted to LICS 2020 - Full versio
Stochastic Games with Disjunctions of Multiple Objectives (Technical Report)
Stochastic games combine controllable and adversarial non-determinism with
stochastic behavior and are a common tool in control, verification and
synthesis of reactive systems facing uncertainty. Multi-objective stochastic
games are natural in situations where several - possibly conflicting -
performance criteria like time and energy consumption are relevant. Such
conjunctive combinations are the most studied multi-objective setting in the
literature. In this paper, we consider the dual disjunctive problem. More
concretely, we study turn-based stochastic two-player games on graphs where the
winning condition is to guarantee at least one reachability or safety objective
from a given set of alternatives. We present a fine-grained overview of
strategy and computational complexity of such \emph{disjunctive queries} (DQs)
and provide new lower and upper bounds for several variants of the problem,
significantly extending previous works. We also propose a novel value
iteration-style algorithm for approximating the set of Pareto optimal
thresholds for a given DQ.Comment: Technical report including appendix with detailed proofs, 29 page
Characterising and Verifying the Core in Concurrent Multi-Player Mean-Payoff Games (Full Version)
Concurrent multi-player mean-payoff games are important models for systems of
agents with individual, non-dichotomous preferences. Whilst these games have
been extensively studied in terms of their equilibria in non-cooperative
settings, this paper explores an alternative solution concept: the core from
cooperative game theory. This concept is particularly relevant for cooperative
AI systems, as it enables the modelling of cooperation among agents, even when
their goals are not fully aligned. Our contribution is twofold. First, we
provide a characterisation of the core using discrete geometry techniques and
establish a necessary and sufficient condition for its non-emptiness. We then
use the characterisation to prove the existence of polynomial witnesses in the
core. Second, we use the existence of such witnesses to solve key decision
problems in rational verification and provide tight complexity bounds for the
problem of checking whether some/every equilibrium in a game satisfies a given
LTL or GR(1) specification. Our approach is general and can be adapted to
handle other specifications expressed in various fragments of LTL without
incurring additional computational costs.Comment: This is the full version of the paper with the same title that
appears in the CSL'24 proceeding