Stochastic structured prediction under bandit feedback follows a learning protocol where on each of a sequence of iterations, the learner receives an input, predicts an output structure, and receives partial feedback in form of a task loss evaluation of the predicted structure. We present applications of this learning scenario to convex and non-convex objectives for structured prediction and analyze them as stochastic first-order methods. We present an experimental evaluation on problems of natural language processing over exponential output spaces, and compare convergence speed across different objectives under the practical criterion of optimal task performance on development data and the optimization-theoretic criterion of minimal squared gradient norm. Best results under both criteria are obtained for a non-convex objective for pairwise preference learning under bandit feedback.

Neural Information Processing Systems http://nips.cc/

Low-rank matrix recovery is a fundamental problem in machine learning with numerous applications. In practice, the problem can be solved by convex optimization namely nuclear norm minimization, or by non-convex optimization as it is well-known that for low-rank matrix problems like matrix sensing and matrix completion, all local optima of the natural non-convex objectives are also globally optimal under certain ideal assumptions.In this paper, we study new approaches for matrix sensing in a semi-random model where an adversary can add any number of arbitrary sensing matrices. More precisely, the problem is to recover a low-rank matrix $X^\star$ from linear measurements $b_i = \langle A_i, X^\star \rangle$, where an unknown subset of the sensing matrices satisfies the Restricted Isometry Property (RIP) and the rest of the $A_i$'s are chosen adversarially.It is known that in the semi-random model, existing non-convex objectives can have bad local optima. To fix this, we present a descent-style algorithm that provably recovers the ground-truth matrix $X^\star$. For the closely-related problem of semi-random matrix completion, prior work [CG18] showed that all bad local optima can be eliminated by reweighting the input data. However, the analogous approach for matrix sensing requires reweighting a set of matrices to satisfy RIP, which is a condition that is NP-hard to check. Instead, we build on the framework proposed in [KLL$^+$23] for semi-random sparse linear regression, where the algorithm in each iteration reweights the input based on the current solution, and then takes a weighted gradient step that is guaranteed to work well locally. Our analysis crucially exploits the connection between sparsity in vector problems and low-rankness in matrix problems, which may have other applications in obtaining robust algorithms for sparse and low-rank problems.

In this paper, we propose a practical online method for solving a class of distributional robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural networks. In the literature, most methods for solving DRO are based on stochastic primal-dual methods. However, primal-dual methods for DRO suffer from several drawbacks: (1) manipulating a high-dimensional dual variable corresponding to the size of data is time expensive; (2) they are not friendly to online learning where data is coming sequentially. To address these issues, we consider a class of DRO with an KL divergence regularization on the dual variables, transform the min-max problem into a compositional minimization problem, and propose practical duality-free online stochastic methods without requiring a large mini-batch size. We establish the state-of-the-art complexities of the proposed methods with and without a Polyak-Łojasiewicz (PL) condition of the objective. Empirical studies on large-scale deep learning tasks (i) demonstrate that our method can speed up the training by more than 2 times than baseline methods and save days of training time on a large-scale dataset with 265K images, and (ii) verify the supreme performance of DRO over Empirical Risk Minimization (ERM) on imbalanced datasets. Of independent interest, the proposed method can be also used for solving a family of stochastic compositional problems with state-of-the-art complexities.

Distributionally Robust Optimization (DRO), which aims to find an optimal decision that minimizes the worst case cost over the ambiguity set of probability distribution, has been applied in diverse applications, e.g., network behavior analysis, risk management, etc. However, existing DRO techniques face three key challenges: 1) how to deal with the asynchronous updating in a distributed environment; 2) how to leverage the prior distribution effectively; 3) how to properly adjust the degree of robustness according to difference scenarios. To this end, we propose an asynchronous distributed algorithm, named Asynchronous Single-looP alternatIve gRadient projEction (ASPIRE) algorithm with the itErative Active SEt method (EASE) to tackle the distributed distributionally robust optimization (DDRO) problem. Furthermore, a new uncertainty set, i.e., constrained $D$-norm uncertainty set, is developed to effectively leverage the prior distribution and flexibly control the degree of robustness. Finally, our theoretical analysis elucidates that the proposed algorithm is guaranteed to converge and the iteration complexity is also analyzed. Extensive empirical studies on real-world datasets demonstrate that the proposed method can not only achieve fast convergence, remain robust against data heterogeneity and malicious attacks, but also tradeoff robustness with performance.

Stochastic structured prediction under bandit feedback follows a learning protocol where on each of a sequence of iterations, the learner receives an input, predicts an output structure, and receives partial feedback in form of a task loss evaluation of the predicted structure. We present applications of this learning scenario to convex and non-convex objectives for structured prediction and analyze them as stochastic first-order methods. We present an experimental evaluation on problems of natural language processing over exponential output spaces, and compare convergence speed across different objectives under the practical criterion of optimal task performance on development data and the optimization-theoretic criterion of minimal squared gradient norm. Best results under both criteria are obtained for a non-convex objective for pairwise preference learning under bandit feedback.

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to stochastic optimization: given an oracle that returns $\alpha$-approximate solutions for distributions over objectives, we compute a distribution over solutions that is $\alpha$-approximate in the worst case. We show that derandomizing this solution is NP-hard in general, but can be done for a broad class of statistical learning tasks. We apply our results to robust neural network training and submodular optimization. We evaluate our approach experimentally on corrupted character classification and robust influence maximization in networks.

Our methods also generalize naturally to let us prove new convergence bounds on low-precision training with other quantization schemes, such as low-precision floating-point computation and logarithmic quantization.

Low-rank matrix recovery is a fundamental problem in machine learning with numerous applications. In practice, the problem can be solved by convex optimization namely nuclear norm minimization, or by non-convex optimization as it is well-known that for low-rank matrix problems like matrix sensing and matrix completion, all local optima of the natural non-convex objectives are also globally optimal under certain ideal assumptions.In this paper, we study new approaches for matrix sensing in a semi-random model where an adversary can add any number of arbitrary sensing matrices. More precisely, the problem is to recover a low-rank matrix X \star from linear measurements b_i \langle A_i, X \star \rangle, where an unknown subset of the sensing matrices satisfies the Restricted Isometry Property (RIP) and the rest of the A_i's are chosen adversarially.It is known that in the semi-random model, existing non-convex objectives can have bad local optima. To fix this, we present a descent-style algorithm that provably recovers the ground-truth matrix X \star . For the closely-related problem of semi-random matrix completion, prior work [CG18] showed that all bad local optima can be eliminated by reweighting the input data.