Algorithms in Strategic or Noisy Environments

Abstract:

Algorithms are often used to interact with agents. When the input is collected from agents instead of being directly given, designing algorithms becomes more challenging. Two main challenges arise here: (i) agents may lie to maximize their own utility functions and we need to take their incentives into account (ii) the uncertainty in agents’ behavior makes the input appear
to be noisy.

In this thesis, we study these two challenges in several contexts: the multi-armed bandit problem, combinatorial auctions and rank aggregation. Our goal is to understand how these strategic and noisy factors make the problem harder and to design new techniques which make algorithms robust against these factors.

In Part I (Chapter 2 and Chapter 3), we study multi-armed bandit algorithms in strategic environments where rewards are decided by actions taken by strategic agents. We show that traditional multi-armed bandit algorithms could fail and we also develop multi-armed bandit algorithms which achieve good performance in strategic envrionments.

In Part II (Chapter 4 and Chapter 5), we focus on combinatorial auctions which are a natural testbed for truthful mechanisms. We characterize the power of truthful mechanisms in several settings and make progress in understanding whether truthful mechanisms are as powerful as algorithms.

In Part III (Chapter 6, Chapter 7 and Chapter 8), we study the top-k ranking problem. In this problem, even if the agents are perfectly incentivzed, their reported comparison results could still be noisy caused by reasons like limit of knowledge and subjective preferences. We design algorithms which aggregate noisy comparisons to output the set of top items.