The goal of continual learning (CL) is to learn different tasks over time. The main desiderata associated with CL are to maintain performance on older tasks, leverage the latter to improve learning of future tasks, and to introduce minimal overhead in the training process (for instance, to not require a growing model or retraining). We propose the Neuro-Inspired Stability-Plasticity Adaptation (NISPA) architecture that addresses these desiderata through a sparse neural network with fixed density. NISPA forms stable paths to preserve learned knowledge from older tasks. Also, NISPA uses connection rewiring to create new plastic paths that reuse existing knowledge on novel tasks. Our extensive evaluation on EMNIST, FashionMNIST, CIFAR10, and CIFAR100 datasets shows that NISPA significantly outperforms representative state-of-the-art continual learning baselines, and it uses up to ten times fewer learnable parameters compared to baselines. We also make the case that sparsity is an essential ingredient for continual learning. The NISPA code is available at https://github.com/BurakGurbuz97/NISPA.

Although learning in high dimensions is commonly believed to suffer from the curse of dimensionality, modern machine learning methods often exhibit an astonishing power to tackle a wide range of challenging real-world learning problems without using abundant amounts of data. How exactly these methods break this curse remains a fundamental open question in the theory of deep learning. While previous efforts have investigated this question by studying the data ($\mathcal D$), model ($\mathcal M$), and inference algorithm ($\mathcal I$) as independent modules, in this paper we analyzes the triplet $(\mathcal D, \mathcal M, \mathcal I)$ as an integrated system and identify important synergies that help mitigate the curse of dimensionality. We first study the basic symmetries associated with various learning algorithms ($\mathcal M, \mathcal I$), focusing on four prototypical architectures in deep learning: fully-connected networks, locally-connected networks, and convolutional networks with and without pooling. We find that learning is most efficient when these symmetries are compatible with those of the data distribution and that performance significantly deteriorates when any member of the \dmi triplet is inconsistent or suboptimal.

Existing auxiliary learning approaches only consider the relationships between the target task and the auxiliary tasks, ignoring the fact that data samples within an auxiliary task could contribute differently to the target task, which results in inefficient auxiliary information usage and non-robustness to data noise. In this paper, we propose to learn a joint task and data schedule for auxiliary learning, which captures the importance of different data samples in each auxiliary task to the target task. However, learning such a joint schedule is challenging due to the large number of additional parameters required for the schedule. To tackle the challenge, we propose a joint task and data scheduling (JTDS) model for auxiliary learning. The JTDS model captures the joint task-data importance through a task-data scheduler, which creates a mapping from task, feature and label information to the schedule in a parameter-efficient way. Particularly, we formulate the scheduler and the task learning process as a bi-level optimization problem. In the lower optimization, the task learning model is updated with the scheduled gradient, while in the upper optimization, the task-data scheduler is updated with the implicit gradient. Experimental results show that our JTDS model significantly outperforms the state-of-the-art methods under supervised, semi-supervised and corrupted label settings.

NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable convergence guarantees for the non-convex objectives. Different from existing NDCG optimization methods, the per-iteration complexity of our algorithms scales with the mini-batch size instead of the number of total items. To improve the effectiveness for deep learning, we further propose practical strategies by using initial warm-up and stop gradient operator. Experimental results on multiple datasets demonstrate that our methods outperform prior ranking approaches in terms of NDCG. To the best of our knowledge, this is the first time that stochastic algorithms are proposed to optimize NDCG with a provable convergence guarantee. Our proposed methods are implemented in the LibAUC library at https://libauc.org.

Sparsely activated transformers, such as Mixture of Experts (MoE), have received great interest due to their outrageous scaling capability which enables dramatical increases in model size without significant increases in computational cost. To achieve this, MoE models replace the feedforward sub-layer with Mixture-of-Experts sub-layer in transformers and use a gating network to route each token to its assigned experts. Since the common practice for efficient training of such models requires distributing experts and tokens across different machines, this routing strategy often incurs huge cross-machine communication cost because tokens and their assigned experts likely reside in different machines. In this paper, we propose \emph{Gating Dropout}, which allows tokens to ignore the gating network and stay at their local machines, thus reducing the cross-machine communication. Similar to traditional dropout, we also show that Gating Dropout has a regularization effect during training, resulting in improved generalization performance. We validate the effectiveness of Gating Dropout on multilingual machine translation tasks. Our results demonstrate that Gating Dropout improves a state-of-the-art MoE model with faster wall-clock time convergence rates and better BLEU scores for a variety of model sizes and datasets.

Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling perturbations from a larger family of distributions. Based on an analysis of DFO for non-convex functions, we propose to choose a distribution for perturbations that minimizes the mean squared error (MSE) of the gradient estimate. We derive three such distributions with provably smaller MSE than Gaussian smoothing. We conduct evaluations of the three sampling distributions on linear regression, reinforcement learning, and DFO benchmarks in order to validate our claims. Our proposal improves on GS with the same computational complexity, and are competitive with and usually outperform Guided ES and Orthogonal ES, two computationally more expensive algorithms that adapt the covariance matrix of normally distributed perturbations.

The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, which extends an existing likelihood-free density ratio estimation method related to probability of improvement (PI). By choosing the utility function for expected improvement (EI), LFBO outperforms the aforementioned method, as well as various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.

Discrete black-box optimization problems are challenging for model-based optimization (MBO) algorithms, such as Bayesian optimization, due to the size of the search space and the need to satisfy combinatorial constraints. In particular, these methods require repeatedly solving a complex discrete global optimization problem in the inner loop, where popular heuristic inner-loop solvers introduce approximations and are difficult to adapt to combinatorial constraints. In response, we propose NN+MILP, a general discrete MBO framework using piecewise-linear neural networks as surrogate models and mixed-integer linear programming (MILP) to optimize the acquisition function. MILP provides optimality guarantees and a versatile declarative language for domain-specific constraints. We test our approach on a range of unconstrained and constrained problems, including DNA binding, constrained binary quadratic problems from the MINLPLib benchmark, and the NAS-Bench-101 neural architecture search benchmark. NN+MILP surpasses or matches the performance of black-box algorithms tailored to the constraints at hand, with global optimization of the acquisition problem running in a few minutes using only standard software packages and hardware.

We consider an online stochastic game with risk-averse agents whose goal is to learn optimal decisions that minimize the risk of incurring significantly high costs. Specifically, we use the Conditional Value at Risk (CVaR) as a risk measure that the agents can estimate using bandit feedback in the form of the cost values of only their selected actions.Since the distributions of the cost functions depend on the actions of all agents that are generally unobservable, they are themselves unknown and, therefore, the CVaR values of the costs are difficult to compute.To address this challenge, we propose a new online risk-averse learning algorithm that relies on one-point zeroth-order estimation of the CVaR gradients computed using CVaR values that are estimated by appropriately sampling the cost functions.We show that this algorithm achieves sub-linear regret with high probability. We also propose two variants of this algorithm that improve performance. The first variant relies on a new sampling strategy that uses samples from the previous iteration to improve the estimation accuracy of the CVaR values. The second variant employs residual feedback that uses CVaR values from the previous iteration to reduce the variance of the CVaR gradient estimates. We theoretically analyze the convergence properties of these variants and illustrate their performance on an online market problem that we model as a Cournot game.

Single-point zeroth-order optimization (SZO) is useful in solving online black-box optimization and control problems in time-varying environments, as it queries the function value only once at each time step. However, the vanilla SZO method is known to suffer from a large estimation variance and slow convergence, which seriously limits its practical application. In this work, we borrow the idea of high-pass and low-pass filters from extremum seeking control (continuous-time version of SZO) and develop a novel SZO method called HLF-SZO by integrating these filters. It turns out that the high-pass filter coincides with the residual feedback method, and the low-pass filter can be interpreted as the momentum method. As a result, the proposed HLF-SZO achieves a much smaller variance and much faster convergence than the vanilla SZO method, and empirically outperforms the residual-feedback SZO method, which are verified via extensive numerical experiments.

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.

Zeroth-order (ZO) method has been shown to be a powerful method for solving the optimization problem where explicit expression of the gradients is difficult or infeasible to obtain. Recently, due to the practical value of the constrained problems, a lot of ZO Frank-Wolfe or projected ZO methods have been proposed. However, in many applications, we may have a very large number of nonconvex white/black-box constraints, which makes the existing zeroth-order methods extremely inefficient (or even not working) since they need to inquire function value of all the constraints and project the solution to the complicated feasible set. In this paper, to solve the nonconvex problem with a large number of white/black-box constraints, we proposed a doubly stochastic zeroth-order gradient method (DSZOG) with momentum method and adaptive step size. Theoretically, we prove DSZOG can converge to the $\epsilon$-stationary point of the constrained problem. Experimental results in two applications demonstrate the superiority of our method in terms of training time and accuracy compared with other ZO methods for the constrained problem.

Max-value entropy search (MES) is one of the state-of-the-art approaches in Bayesian optimization (BO). In this paper, we propose a novel variant of MES for constrained problems, called Constrained MES via Information lower BOund (CMES-IBO), that is based on a Monte Carlo (MC) estimator of a lower bound of a mutual information (MI). Unlike existing studies, our MI is defined so that uncertainty with respect to feasibility can be incorporated. We derive a lower bound of the MI that guarantees non-negativity, while a constrained counterpart of conventional MES can be negative. We further provide theoretical analysis that assures the low-variability of our estimator which has never been investigated for any existing information-theoretic BO. Moreover, using the conditional MI, we extend CMES-IBO to the parallel setting while maintaining the desirable properties. We demonstrate the effectiveness of CMES-IBO by several benchmark functions and real-world problems.

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration complexity, and propose a generic approach that, based on optimal first-order methods, allows to obtain in a black-box fashion new zeroth-order algorithms for non-smooth convex optimization problems. Our approach not only leads to optimal oracle complexity, but also allows to obtain iteration complexity similar to first-order methods, which, in turn, allows to exploit parallel computations to accelerate the convergence of our algorithms. We also elaborate on extensions for stochastic optimization problems, saddle-point problems, and distributed optimization.