[Paper Review] Competing Prediction Algorithms

Omer Ben-Porat, Moshe Tennenholtz|arXiv (Cornell University)|Jun 5, 2018

Auction Theory and Applications18 references3 citations

TL;DR

This paper introduces a game-theoretic framework for competing prediction algorithms in a PAC-learning setting, where players strategically optimize predictions to maximize user selection. It proves that pure Nash equilibria (PNE) always exist in the empirical game, and better-response dynamics converge to an approximate PNE with high probability using a small number of samples.

ABSTRACT

Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products, the strategic use of prediction algorithms remains unexplored. The goal of this paper is to examine strategic use of prediction algorithms. We introduce a novel game-theoretic setting that is based on the PAC learning framework, where each player (aka a prediction algorithm at competition) seeks to maximize the sum of points for which it produces an accurate prediction and the others do not. We show that algorithms aiming at generalization may wittingly miss-predict some points to perform better than others on expectation. We analyze the empirical game, i.e. the game induced on a given sample, prove that it always possesses a pure Nash equilibrium, and show that every better-response learning process converges. Moreover, our learning-theoretic analysis suggests that players can, with high probability, learn an approximate pure Nash equilibrium for the whole population using a small number of samples.

Motivation & Objective

• To study the strategic behavior of prediction algorithms in competitive online environments where companies vie for user selection based on predictive accuracy.
• To model the competition between prediction algorithms as a game where payoff depends on users selecting the best-fitting product among multiple offers.
• To investigate whether pure Nash equilibria exist in such games and whether learning dynamics can efficiently converge to approximate equilibria.
• To analyze the generalization of empirical equilibria to the full population distribution, especially under bounded and unbounded hypothesis class capacities.

Proposed method

• Formalizes a game-theoretic model based on the PAC learning framework, where each player's strategy is a predictive function over user instances.
• Defines a player's payoff as the expected number of users who select her product, where users select uniformly at random among all products within their threshold of acceptability.
• Proves uniform convergence of empirical payoffs to true payoffs over all strategy profiles under bounded pseudo-dimension, ensuring reliable empirical estimation.
• Demonstrates that every empirical game (induced on a finite sample) possesses a pure Nash equilibrium, even with strategic misprediction.
• Establishes convergence of better-response dynamics to an approximate PNE in polynomial time with high probability using sample-based learning.
• Analyzes the non-learnability of equilibria in infinite-capacity settings, showing that empirical PNEs may not generalize to the full population.

Experimental results

Research questions

• RQ1 Does a pure Nash equilibrium exist in the game of competing prediction algorithms under the PAC learning framework?
• RQ2 Can players efficiently learn an approximate pure Nash equilibrium using only a small number of samples from the underlying distribution?
• RQ3 Does better-response dynamics converge to an approximate PNE in this strategic prediction setting?
• RQ4 Under what conditions does an empirical pure Nash equilibrium generalize to an approximate pure Nash equilibrium on the full population?
• RQ5 How does strategic misprediction—deliberately missing predictions to outperform competitors—affect equilibrium outcomes?

Key findings

• The empirical game induced on any finite sample always possesses a pure Nash equilibrium, even when players strategically mispredict.
• Better-response learning dynamics converge to an approximate pure Nash equilibrium in polynomial time with high probability over the sample draw.
• Players can learn an approximate PNE for the full population using only a small number of samples, due to uniform convergence of payoffs across strategy profiles.
• In the case of bounded pseudo-dimension, empirical payoffs uniformly concentrate around true payoffs, enabling reliable learning from samples.
• In infinite-capacity settings, even when the underlying distribution is known, empirical PNEs may fail to generalize to the full population with high probability.
• Strategic behavior can lead to suboptimal individual strategies even when players have full knowledge of the distribution and other players’ strategy spaces.