Response Prediction for Low-Regret Agents

TL;DR

This paper develops a theoretical framework to predict advertiser responses in auction settings by modeling their decision-making as a low-regret strategy in a costly, dynamic multi-armed bandit scenario, enabling impact assessment of auction rule changes.

Contribution

It introduces a novel approach to predict agent actions in uncertain environments by linking their low-regret strategies to regret bounds in a multi-armed bandit model.

Findings

The framework can predict agent actions with regret bounds depending on the agent's strategy.

It demonstrates how to learn to play bandits with regret bounds without observing rewards.

The approach accounts for changing costs and unobserved stochastic rewards.

Abstract

Companies like Google and Microsoft run billions of auctions every day to sell advertising opportunities. Any change to the rules of these auctions can have a tremendous effect on the revenue of the company and the welfare of the advertisers and the users. Therefore, any change requires careful evaluation of its potential impacts. Currently, such impacts are often evaluated by running simulations or small controlled experiments. This, however, misses the important factor that the advertisers respond to changes. Our goal is to build a theoretical framework for predicting the actions of an agent (the advertiser) that is optimizing her actions in an uncertain environment. We model this problem using a variant of the multi-armed bandit setting where playing an arm is costly. The cost of each arm changes over time and is publicly observable. The value of playing an arm is drawn stochastically from a static distribution and is observed by the agent and not by us. We, however, observe the actions of the agent. Our main result is that assuming the agent is playing a strategy with a regret of at most $f(T)$ within the first $T$ rounds, we can learn to play the multi-armed bandits game (without observing the rewards) in such a way that the regret of our selected actions is at most $O(k^4(f(T)+1)\log(T))$, where $k$ is the number of arms.