Publications

Hypergradients and an optimization method for bilevel problems whose inner solutions form a manifold.

Combines zeroth-order leader updates with a Frank–Wolfe equilibrium solver to tune network tolls, capacities, or incentives without differentiating through users’ congestion equilibria.

Establishes matching bounds on the stochastic-gradient queries needed under a local α-Polyak–Łojasiewicz condition (1 ≤ α < 2), with a variance-reduced method attaining the rate. The guarantees assume initialization near a component of local minimizers and that iterates remain nearby with high probability.

Using curvature information to improve sample complexity under gradient dominance, with applications to reinforcement learning.

An auxiliary-distribution approach to generalization bounds using Jensen–Shannon and Rényi information, including settings with different training and test distributions.

Connects f-divergences and generalized rate-distortion theory to bounds for lossy compression and the generalization error of learning algorithms.

Uses rate-distortion theory to study generalization error when training and test distributions differ, and to quantify the effects of model misspecification.

Sharp complexity limits for first-order methods when the gradient dominance condition holds on a sublevel set.

SQ-G tackles bilevel optimization with multiple lower-level minimizers by approximating the worst upper-level outcome through Langevin sampling and an upper-tail loss average. Under parameter-uniform local PL and additional assumptions, we establish approximation and optimization guarantees with explicit dependence on the minimizer manifold’s intrinsic dimension.

Projection-free methods for optimization with functional constraints, motivated by risk aversion and sparsity.