Andrew Lowy — Page 2

arXiv2023

A Stochastic Optimization Framework for Fair Risk Minimization

Despite the success of large-scale empirical risk minimization (ERM) at achieving high accuracy across a variety of machine learning tasks, fair ERM is hindered by the incompatibility of fairness constraints with stochastic optimization. We consider the problem of fair classification with discrete sensitive attributes and potentially large models and data sets, requiring stochastic solvers. Existing in-processing fairness algorithms are either impractical in the large-scale setting because they require large batches of data at each iteration or they are not guaranteed to converge. In this paper, we develop the first stochastic in-processing fairness algorithm with guaranteed convergence. For demographic parity, equalized odds, and equal opportunity notions of fairness, we provide slight variations of our algorithm--called FERMI--and prove that each of these variations converges in stochastic optimization with any batch size. Empirically, we show that FERMI is amenable to stochastic solvers with multiple (non-binary) sensitive attributes and non-binary targets, performing well even with minibatch size as small as one. Extensive experiments show that FERMI achieves the most favorable tradeoffs between fairness violation and test accuracy across all tested setups compared with state-of-the-art baselines for demographic parity, equalized odds, equal opportunity. These benefits are especially significant with small batch sizes and for non-binary classification with large number of sensitive attributes, making FERMI a practical, scalable fairness algorithm. The code for all of the experiments in this paper is available at: https://github.com/optimization-for-data-driven-science/FERMI.

cs.LG↗

arXiv2021

Efficient Search of First-Order Nash Equilibria in Nonconvex-Concave Smooth Min-Max Problems

We propose an efficient algorithm for finding first-order Nash equilibria in min-max problems of the form $\min_{x \in X}\max_{y\in Y} F(x,y)$, where the objective function is smooth in both variables and concave with respect to $y$; the sets $X$ and $Y$ are convex and "projection-friendly," and $Y$ is compact. Our goal is to find an $(\varepsilon_x,\varepsilon_y)$-first-order Nash equilibrium with respect to a stationarity criterion that is stronger than the commonly used proximal gradient norm. The proposed approach is fairly simple: we perform approximate proximal-point iterations on the primal function, with inexact oracle provided by Nesterov's algorithm run on the regularized function $F(x_t,\cdot)$, $x_t$ being the current primal iterate. The resulting iteration complexity is $O(\varepsilon_x{}^{-2} \varepsilon_y{}^{-1/2})$ up to a logarithmic factor. As a byproduct, the choice $\varepsilon_y = O(\varepsilon_x{}^2)$ allows for the $O(\varepsilon_x{}^{-3})$ complexity of finding an $\varepsilon_x$-stationary point for the standard Moreau envelope of the primal function. Moreover, when the objective is strongly concave with respect to $y$, the complexity estimate for our algorithm improves to $O(\varepsilon_x{}^{-2}{κ_y}^{1/2})$ up to a logarithmic factor, where $κ_y$ is the condition number appropriately adjusted for coupling. In both scenarios, the complexity estimates are the best known so far, and are only known for the (weaker) proximal gradient norm criterion. Meanwhile, our approach is "user-friendly:" (i) the algorithm is built upon running a variant of Nesterov's accelerated algorithm as subroutine and avoids extragradient steps; (ii) the convergence analysis recycles the well-known results on accelerated methods with inexact oracle. Finally, we extend the approach to non-Euclidean proximal geometries.

math.OC↗