1,140 research outputs found
Convergence-Optimal Quantizer Design of Distributed Contraction-based Iterative Algorithms with Quantized Message Passing
In this paper, we study the convergence behavior of distributed iterative
algorithms with quantized message passing. We first introduce general iterative
function evaluation algorithms for solving fixed point problems distributively.
We then analyze the convergence of the distributed algorithms, e.g. Jacobi
scheme and Gauss-Seidel scheme, under the quantized message passing. Based on
the closed-form convergence performance derived, we propose two quantizer
designs, namely the time invariant convergence-optimal quantizer (TICOQ) and
the time varying convergence-optimal quantizer (TVCOQ), to minimize the effect
of the quantization error on the convergence. We also study the tradeoff
between the convergence error and message passing overhead for both TICOQ and
TVCOQ. As an example, we apply the TICOQ and TVCOQ designs to the iterative
waterfilling algorithm of MIMO interference game.Comment: 17 pages, 9 figures, Transaction on Signal Processing, accepte
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
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
Towards a science of security games
Abstract. Security is a critical concern around the world. In many domains from counter-terrorism to sustainability, limited security resources prevent complete security coverage at all times. Instead, these limited resources must be scheduled (or allocated or deployed), while simultaneously taking into account the impor-tance of different targets, the responses of the adversaries to the security posture, and the potential uncertainties in adversary payoffs and observations, etc. Com-putational game theory can help generate such security schedules. Indeed, casting the problem as a Stackelberg game, we have developed new algorithms that are now deployed over multiple years in multiple applications for scheduling of secu-rity resources. These applications are leading to real-world use-inspired research in the emerging research area of âsecurity gamesâ. The research challenges posed by these applications include scaling up security games to real-world sized prob-lems, handling multiple types of uncertainty, and dealing with bounded rationality of human adversaries.
Adversarial Bandits with Knapsacks
We consider Bandits with Knapsacks (henceforth, BwK), a general model for
multi-armed bandits under supply/budget constraints. In particular, a bandit
algorithm needs to solve a well-known knapsack problem: find an optimal packing
of items into a limited-size knapsack. The BwK problem is a common
generalization of numerous motivating examples, which range from dynamic
pricing to repeated auctions to dynamic ad allocation to network routing and
scheduling. While the prior work on BwK focused on the stochastic version, we
pioneer the other extreme in which the outcomes can be chosen adversarially.
This is a considerably harder problem, compared to both the stochastic version
and the "classic" adversarial bandits, in that regret minimization is no longer
feasible. Instead, the objective is to minimize the competitive ratio: the
ratio of the benchmark reward to the algorithm's reward.
We design an algorithm with competitive ratio O(log T) relative to the best
fixed distribution over actions, where T is the time horizon; we also prove a
matching lower bound. The key conceptual contribution is a new perspective on
the stochastic version of the problem. We suggest a new algorithm for the
stochastic version, which builds on the framework of regret minimization in
repeated games and admits a substantially simpler analysis compared to prior
work. We then analyze this algorithm for the adversarial version and use it as
a subroutine to solve the latter.Comment: Extended abstract appeared in FOCS 201
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