arXiv subjects

Karel Horák

Publications and source records attributed to Karel Horák.

3 recordsLinked to original sources

arXiv2020

Solving Zero-Sum One-Sided Partially Observable Stochastic Games

Many security and other real-world situations are dynamic in nature and can be modelled as strictly competitive (or zero-sum) dynamic games. In these domains, agents perform actions to affect the environment and receive observations -- possibly imperfect -- about the situation and the effects of the opponent's actions. Moreover, there is no limitation on the total number of actions an agent can perform -- that is, there is no fixed horizon. These settings can be modelled as partially observable stochastic games (POSGs). However, solving general POSGs is computationally intractable, so we focus on a broad subclass of POSGs called one-sided POSGs. In these games, only one agent has imperfect information while their opponent has full knowledge of the current situation. We provide a full picture for solving one-sided POSGs: we (1) give a theoretical analysis of one-sided POSGs and their value functions, (2) show that a variant of a value-iteration algorithm converges in this setting, (3) adapt the heuristic search value-iteration algorithm for solving one-sided POSGs, (4) describe how to use approximate value functions to derive strategies in the game, and (5) demonstrate that our algorithm can solve one-sided POSGs of non-trivial sizes and analyze the scalability of our algorithm in three different domains: pursuit-evasion, patrolling, and search games.

cs.GT↗

arXiv2019

Compact Representation of Value Function in Partially Observable Stochastic Games

Value methods for solving stochastic games with partial observability model the uncertainty about states of the game as a probability distribution over possible states. The dimension of this belief space is the number of states. For many practical problems, for example in security, there are exponentially many possible states which causes an insufficient scalability of algorithms for real-world problems. To this end, we propose an abstraction technique that addresses this issue of the curse of dimensionality by projecting high-dimensional beliefs to characteristic vectors of significantly lower dimension (e.g., marginal probabilities). Our two main contributions are (1) novel compact representation of the uncertainty in partially observable stochastic games and (2) novel algorithm based on this compact representation that is based on existing state-of-the-art algorithms for solving stochastic games with partial observability. Experimental evaluation confirms that the new algorithm over the compact representation dramatically increases the scalability compared to the state of the art.

cs.GT↗

arXiv2016

Dynamic Programming for One-Sided Partially Observable Pursuit-Evasion Games

Pursuit-evasion scenarios appear widely in robotics, security domains, and many other real-world situations. We focus on two-player pursuit-evasion games with concurrent moves, infinite horizon, and discounted rewards. We assume that the players have a partial observability, however, the evader is given an advantage of knowing the current position of the units of the pursuer. This setting is particularly interesting for security domains where a robust strategy, designed to maximize the utility in the worst-case scenario, is often desirable. We provide, to the best of our knowledge, the first algorithm that provably converges to the value of a partially observable pursuit-evasion game with infinite horizon. Our algorithm extends well-known value iteration algorithm by exploiting that (1) the value functions of our game depend only on position of the pursuer and the belief he has about the current position of the evader, and (2) that these functions are piecewise linear and convex in the belief space.

cs.GT↗