Continuous Value Function Approximation for Sequential Bidding Policies

TL;DR

This paper introduces a continuous approximation method for dynamic programming models in sequential bidding, using grid-based piecewise linear value function approximations to reduce computational costs.

Contribution

It proposes a novel continuous approximation approach for dynamic programming in sequential auctions, enabling more efficient computation of bidding policies.

Findings

Significant computational savings achieved

Small loss in solution quality with the approximation

Effective handling of complementarities and substitutability in resources

Abstract

Market-based mechanisms such as auctions are being studied as an appropriate means for resource allocation in distributed and mulitagent decision problems. When agents value resources in combination rather than in isolation, they must often deliberate about appropriate bidding strategies for a sequence of auctions offering resources of interest. We briefly describe a discrete dynamic programming model for constructing appropriate bidding policies for resources exhibiting both complementarities and substitutability. We then introduce a continuous approximation of this model, assuming that money (or the numeraire good) is infinitely divisible. Though this has the potential to reduce the computational cost of computing policies, value functions in the transformed problem do not have a convenient closed form representation. We develop {em grid-based} approximation for such value functions, representing value functions using piecewise linear approximations. We show that these methods can offer significant computational savings with relatively small cost in solution quality.