Adaptive Uncertainty Resolution in Bayesian Combinatorial Optimization Problems

TL;DR

This paper investigates the value of adaptive versus non-adaptive observations in Bayesian combinatorial optimization problems with uncertain parameters, providing approximation techniques and bounds on adaptivity benefits.

Contribution

The paper introduces a unifying approach to approximate optimal observation schemes and quantifies the limited advantage of adaptivity in these problems.

Findings

Probing significantly improves system performance.

Adaptivity offers only constant-factor improvements.

The techniques relate to outlier versions of deterministic optimization.

Abstract

In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some objective function over the parameters) is significantly improved if some of these parameters can be probed or observed. In a resource constrained situation, deciding which parameters to observe in order to optimize system performance itself becomes an interesting and important optimization problem. This general problem is the focus of this paper. One of the most important considerations in this framework is whether adaptivity is required for the observations. Adaptive observations introduce blocking or sequential operations in the system whereas non-adaptive observations can be performed in parallel. One of the important questions in this regard is to characterize the benefit of adaptivity for probes and observation. We present general techniques for designing constant factor approximations to the optimal observation schemes for several widely used scheduling and metric objective functions. We show a unifying technique that relates this optimization problem to the outlier version of the corresponding deterministic optimization. By making this connection, our technique shows constant factor upper bounds for the benefit of adaptivity of the observation schemes. We show that while probing yields significant improvement in the objective function, being adaptive about the probing is not beneficial beyond constant factors.