Related papers: Optimistic bounds for multi-output prediction

We consider the problem of multi-fidelity zeroth-order optimization, where one can evaluate a function $f$ at various approximation levels (of varying costs), and the goal is to optimize $f$ with the cheapest evaluations possible. In this…

The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the method is presented with three different finite procedures for…

We present a bound for value-prediction error with respect to model misspecification that is tight, including constant factors. This is a direct improvement of the "simulation lemma," a foundational result in reinforcement learning. We…

This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight…

We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in…

In this paper, we propose a new framework to study the generalization property of classifier chains trained over observations associated with multiple and interdependent class labels. The results are based on large deviation inequalities…

First order methods endowed with global convergence guarantees operate using global lower bounds on the objective. The tightening of the bounds has been shown to increase both the theoretical guarantees and the practical performance. In…

We introduce in this paper an optimal first-order method that allows an easy and cheap evaluation of the local Lipschitz constant of the objective's gradient. This constant must ideally be chosen at every iteration as small as possible,…

In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…

We consider the classical problem of sequential probability assignment under logarithmic loss while competing against an arbitrary, potentially nonparametric class of experts. We obtain tight bounds on the minimax regret via a new approach…

The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic…

We consider non-smooth saddle point optimization problems. To solve these problems, we propose a zeroth-order method under bounded or Lipschitz continuous noise, possible adversarial. In contrast to the state-of-the-art algorithms, our…

We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without…

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…

This paper focuses on developing a conditional gradient algorithm for multiobjective optimization problems with an unbounded feasible region. We employ the concept of recession cone to establish the well-defined nature of the algorithm. The…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

In this work, we propose a framework to learn feedback control policies with guarantees on closed-loop generalization and adversarial robustness. These policies are learned directly from expert demonstrations, contained in a dataset of…

This paper proposes a class of well-conditioned neural networks in which a unit amount of change in the inputs causes at most a unit amount of change in the outputs or any of the internal layers. We develop the known methodology of…

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset…

Boosting algorithms produce a classifier by iteratively combining base hypotheses. It has been observed experimentally that the generalization error keeps improving even after achieving zero training error. One popular explanation…