Most of the literature on neural network quantization requires some training of the quantized model (fine-tuning). However, this training is not always possible in real-world scenarios, as it requires the full dataset. Lately, post-training quantization methods have gained considerable attention, as they are simple to use and require only a small, unlabeled calibration set. Yet, they usually incur significant accuracy degradation when quantized below 8-bits. This paper seeks to address this problem by introducing two pipelines, advanced and light, where the former involves: (i) minimizing the quantization errors of each layer by optimizing its parameters over the calibration set; (ii) using integer programming to optimally allocate the desired bit-width for each layer while constraining accuracy degradation or model compression; and (iii) tuning the mixed-precision model statistics to correct biases introduced during quantization. While the light pipeline which invokes only (ii) and (iii) obtains surprisingly accurate results; the advanced pipeline yields state-of-the-art accuracy-compression ratios for both vision and text models. For instance, on ResNet50, we obtain less than 1% accuracy degradation while compressing the model to 13% of its original size. We open-sourced our code.

We propose a novel Bayesian method to solve the maximization of a time-dependent expensive-to-evaluate oracle. We are interested in the decision that maximizes the oracle at a finite time horizon, when relatively few noisy evaluations can be performed before the horizon. Our recursive, two-step lookahead expected payoff ($\texttt{r2LEY}$) acquisition function makes nonmyopic decisions at every stage by maximizing the estimated expected value of the oracle at the horizon. $\texttt{r2LEY}$ circumvents the evaluation of the expensive multistep (more than two steps) lookahead acquisition function by recursively optimizing a two-step lookahead acquisition function at every stage; unbiased estimators of this latter function and its gradient are utilized for efficient optimization. $\texttt{r2LEY}$ is shown to exhibit natural exploration properties far from the time horizon, enabling accurate emulation of the oracle, which is exploited in the final decision made at the horizon. To demonstrate the utility of $\texttt{r2LEY}$, we compare it with time-dependent extensions of popular myopic acquisition functions via both synthetic and real-world datasets.

In this paper, we propose the novel model of combinatorial pure exploration with partial linear feedback (CPE-PL). In CPE-PL, given a combinatorial action space $\mathcal{X} \subseteq \{0,1\}^d$, in each round a learner chooses one action $x \in \mathcal{X}$ to play, obtains a random (possibly nonlinear) reward related to $x$ and an unknown latent vector $\theta \in \mathbb{R}^d$, and observes a partial linear feedback $M_{x} (\theta + \eta)$, where $\eta$ is a zero-mean noise vector and $M_x$ is a transformation matrix for $x$. The objective is to identify the optimal action with the maximum expected reward using as few rounds as possible. We also study the important subproblem of CPE-PL, i.e., combinatorial pure exploration with full-bandit feedback (CPE-BL), in which the learner observes full-bandit feedback (i.e. $M_x = x^{\top}$) and gains linear expected reward $x^{\top} \theta$ after each play. In this paper, we first propose a polynomial-time algorithmic framework for the general CPE-PL problem with novel sample complexity analysis. Then, we propose an adaptive algorithm dedicated to the subproblem CPE-BL with better sample complexity. Our work provides a novel polynomial-time solution to simultaneously address limited feedback, general reward function and combinatorial action space including matroids, matchings, and $s$-$t$ paths.

We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order smoothness properties of the function on the optimization error and on the cumulative regret. To solve this problem we consider a randomized approximation of the projected gradient descent algorithm. The gradient is estimated by a randomized procedure involving two function evaluations and a smoothing kernel. We derive upper bounds for this algorithm both in the constrained and unconstrained settings and prove minimax lower bounds for any sequential search method. Our results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters. Based on this algorithm, we also propose an estimator of the minimum value of the function achieving almost sharp oracle behavior. We compare our results with the state-of-the-art, highlighting a number of key improvements.

Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), as the widely employed policy based reinforcement learning (RL) methods, are prone to converge to a sub-optimal solution as they limit the policy representation to a particular parametric distribution class. To address this issue, we develop an innovative Optimistic Distributionally Robust Policy Optimization (ODRPO) algorithm, which effectively utilizes Optimistic Distributionally Robust Optimization (DRO) approach to solve the trust region constrained optimization problem without parameterizing the policies. Our algorithm improves TRPO and PPO with a higher sample efficiency and a better performance of the final policy while attaining the learning stability. Moreover, it achieves a globally optimal policy update that is not promised in the prevailing policy based RL algorithms. Experiments across tabular domains and robotic locomotion tasks demonstrate the effectiveness of our approach.

Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as a mixed-integer program with an objective function composed of a convex quadratic loss function and a regularization penalty subject to linear constraints. The optimal solution to this mathematical program is known to have desirable statistical properties under certain conditions. However, the state-of-the-art optimization solvers are not able to obtain provably optimal solutions to the existing mathematical formulations for medium-size problems within reasonable computational times. To address this difficulty, we tackle the problem from both computational and statistical perspectives. On the one hand, we propose a concrete early stopping criterion to terminate the branch-and-bound process in order to obtain a near-optimal solution to the mixed-integer program, and establish the consistency of this approximate solution. On the other hand, we improve the existing formulations by replacing the linear "big-$M$" constraints that represent the relationship between the continuous and binary indicator variables with second-order conic constraints. Our numerical results demonstrate the effectiveness of the proposed approaches.

Existing research into online multi-label classification, such as online sequential multi-label extreme learning machine (OSML-ELM) and stochastic gradient descent (SGD), has achieved promising performance. However, these works do not take label dependencies into consideration and lack a theoretical analysis of loss functions. Accordingly, we propose a novel online metric learning paradigm for multi-label classification to fill the current research gap. Generally, we first propose a new metric for multi-label classification which is based on $k$-Nearest Neighbour ($k$NN) and combined with large margin principle. Then, we adapt it to the online settting to derive our model which deals with massive volume ofstreaming data at a higher speed online. Specifically, in order to learn the new $k$NN-based metric, we first project instances in the training dataset into the label space, which make it possible for the comparisons of instances and labels in the same dimension. After that, we project both of them into a new lower dimension space simultaneously, which enables us to extract the structure of dependencies between instances and labels. Finally, we leverage the large margin and $k$NN principle to learn the metric with an efficient optimization algorithm. Moreover, we provide theoretical analysis on the upper bound of the cumulative loss for our method. Comprehensive experiments on a number of benchmark multi-label datasets validate our theoretical approach and illustrate that our proposed online metric learning (OML) algorithm outperforms state-of-the-art methods.

This paper is an in-depth investigation of using kernel methods to immunize optimization solutions against distributional ambiguity. We propose kernel distributionally robust optimization (K-DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct ambiguity sets. It can be reformulated as a tractable program by using the conic duality of moment problems and an extension of the RKHS representer theorem. Our insights reveal that universal RKHSs are large enough for K-DRO to be effective. This paper provides both theoretical analyses that extend the robustness properties of kernel methods, as well as practical algorithms that can be applied to general optimization problems, not limited to kernelized models.

We propose a novel technique that can generate natural-looking adversarial examples by bounding the variations induced for internal activation values in some deep layer(s), through a distribution quantile bound and a polynomial barrier loss function. By bounding model internals instead of individual pixels, our attack admits perturbations closely coupled with the existing features of the original input, allowing the generated examples to be natural-looking while having diverse and often substantial pixel distances from the original input. Enforcing per-neuron distribution quantile bounds allows addressing the non-uniformity of internal activation values. Our evaluation on ImageNet and five different model architecture demonstrates that our attack is quite effective. Compared to the state-of-the-art pixel space attack, semantic attack, and feature space attack, our attack can achieve the same attack success/confidence level while having much more natural-looking adversarial perturbations. These perturbations piggy-back on existing local features and do not have any fixed pixel bounds.

The multi-level, multi-disciplinary and multi-fidelity optimization framework developed at Bombardier Aviation has shown great results to explore efficient and competitive aircraft configurations. This optimization framework has been developed within the Isight software, the latter offers a set of ready-to-use optimizers. Unfortunately, the computational effort required by the Isight optimizers can be prohibitive with respect to the requirements of an industrial context. In this paper, a constrained Bayesian optimization optimizer, namely the super efficient global optimization with mixture of experts, is used to reduce the optimization computational effort. The obtained results showed significant improvements compared to two of the popular Isight optimizers. The capabilities of the tested constrained Bayesian optimization solver are demonstrated on Bombardier research aircraft configuration study cases.