An Adversarial Interpretation of Information-Theoretic Bounded Rationality

Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decision-making against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker's payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory.Comment: 7 pages, 4 figures. Proceedings of AAAI-1

Rational Value of Information Estimation for Measurement Selection

Computing value of information (VOI) is a crucial task in various aspects of decision-making under uncertainty, such as in meta-reasoning for search; in selecting measurements to make, prior to choosing a course of action; and in managing the exploration vs. exploitation tradeoff. Since such applications typically require numerous VOI computations during a single run, it is essential that VOI be computed efficiently. We examine the issue of anytime estimation of VOI, as frequently it suffices to get a crude estimate of the VOI, thus saving considerable computational resources. As a case study, we examine VOI estimation in the measurement selection problem. Empirical evaluation of the proposed scheme in this domain shows that computational resources can indeed be significantly reduced, at little cost in expected rewards achieved in the overall decision problem.Comment: 7 pages, 2 figures, presented at URPDM2010; plots fixe

Are Consumers Fooled by Discounts? An Experimental Test in a Consumer Search Environment

In this paper we investigate experimentally if people search optimally and how price promotions influence search behavior. We implement a sequential search task with exogenous price dispersion in a baseline treatment and introduce discounts in two experimental treatments. We find that search behavior is roughly consistent with optimal search but also observe some discount biases. If subjects don't know in advance where discounts are offered the purchase probability is increased by 19 percentage points in shops with discounts, even after controlling for the benefit of the discount and for risk preferences. If consumers know in advance where discounts are given then the bias is only weakly significant and much smaller (7 percentage points).Consumer Search Theory, Search Cost, Price Promotion