4,138 research outputs found
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
Equilibrium Computation and Robust Optimization in Zero Sum Games with Submodular Structure
We define a class of zero-sum games with combinatorial structure, where the
best response problem of one player is to maximize a submodular function. For
example, this class includes security games played on networks, as well as the
problem of robustly optimizing a submodular function over the worst case from a
set of scenarios. The challenge in computing equilibria is that both players'
strategy spaces can be exponentially large. Accordingly, previous algorithms
have worst-case exponential runtime and indeed fail to scale up on practical
instances. We provide a pseudopolynomial-time algorithm which obtains a
guaranteed -approximate mixed strategy for the maximizing player.
Our algorithm only requires access to a weakened version of a best response
oracle for the minimizing player which runs in polynomial time. Experimental
results for network security games and a robust budget allocation problem
confirm that our algorithm delivers near-optimal solutions and scales to much
larger instances than was previously possible.Comment: 20 pages, 8 figures. A shorter version of this paper appears at AAAI
201
Non-additive Security Games
We have investigated the security game under non-additive utility functions
Designing the Game to Play: Optimizing Payoff Structure in Security Games
Effective game-theoretic modeling of defender-attacker behavior is becoming
increasingly important. In many domains, the defender functions not only as a
player but also the designer of the game's payoff structure. We study
Stackelberg Security Games where the defender, in addition to allocating
defensive resources to protect targets from the attacker, can strategically
manipulate the attacker's payoff under budget constraints in weighted L^p-norm
form regarding the amount of change. Focusing on problems with weighted
L^1-norm form constraint, we present (i) a mixed integer linear program-based
algorithm with approximation guarantee; (ii) a branch-and-bound based algorithm
with improved efficiency achieved by effective pruning; (iii) a polynomial time
approximation scheme for a special but practical class of problems. In
addition, we show that problems under budget constraints in L^0-norm form and
weighted L^\infty-norm form can be solved in polynomial time. We provide an
extensive experimental evaluation of our proposed algorithms
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