The deployment of ever-larger machine learning models reflects a growing consensus that the more expressive the model class one optimizes over—and the more data one has access to—the more one can improve performance. As models get deployed in a variety of real-world scenarios, they inevitably face strategic environments. In this work, we consider the natural question of how the interplay of models and strategic interactions affects the relationship between performance at equilibrium and the expressivity of model classes. We find that strategic interactions can break the conventional view—meaning that performance does not necessarily monotonically improve as model classes get larger or more expressive (even with infinite data). We show the implications of this result in several contexts including strategic regression, strategic classification, and multi-agent reinforcement learning. In particular, we show that each of these settings admits a Braess' paradox-like phenomenon in which optimizing over less expressive model classes allows one to achieve strictly better equilibrium outcomes. Motivated by these examples, we then propose a new paradigm for model selection in games wherein an agent seeks to choose amongst different model classes to use as their action set in a game.

The combination of the Bayesian game and learning has a rich history, with the idea of controlling a single agent in a system composed of multiple agents with unknown behaviors given a set of types, each specifying a possible behavior for the other agents. The idea is to plan an agent's own actions with respect to those types which it believes are most likely to maximize the payoff. However, the type beliefs are often learned from past actions and likely to be incorrect. With this perspective in mind, we consider an agent in a game with type predictions of other components, and investigate the impact of incorrect beliefs to the agent’s payoff. In particular, we formally define a tradeoff between risk and opportunity by comparing the payoff obtained against the optimal payoff, which is represented by a gap caused by trusting or distrusting the learned beliefs.Our main results characterize the tradeoff by establishing upper and lower bounds on the Pareto front for both normal-form and stochastic Bayesian games, with numerical results provided.

We consider the problem of convex function chasing with black-box advice, where an online decision-maker aims to minimize the total cost of making and switching between decisions in a normed vector space, aided by black-box advice such as the decisions of a machine-learned algorithm. The decision-maker seeks cost comparable to the advice when it performs well, known as \emph{consistency}, while also ensuring worst-case \emph{robustness} even when the advice is adversarial. We first consider the common paradigm of algorithms that switch between the decisions of the advice and a competitive algorithm, showing that no algorithm in this class can improve upon 3-consistency while staying robust. We then propose two novel algorithms that bypass this limitation by exploiting the problem’s convexity. The first, $\textsc{Interp}$, achieves $(\sqrt{2}+\epsilon)$-consistency and $\mathcal{O}(\frac{C}{\epsilon^2})$-robustness for any $\epsilon > 0$, where $C$ is the competitive ratio of an algorithm for convex function chasing or a subclass thereof. The second, $\textsc{BdInterp}$, achieves $(1+\epsilon)$-consistency and $\mathcal{O}(\frac{CD}{\epsilon})$-robustness when the problem has bounded diameter $D$. Further, we show that $\textsc{BdInterp}$ achieves near-optimal consistency-robustness trade-off for the special case where cost functions are $\alpha$-polyhedral.