NeurIPS 2023 Papers

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the limited availability of real-world instances often leads to sub-optimal decisions and biased solver assessments, which motivates a suite of synthetic MILP instance generation techniques. However, existing methods either rely heavily on expert-designed formulations or struggle to capture the rich features of real-world instances. To tackle this problem, we propose G2MILP, *the first* deep generative framework for MILP instances. Specifically, G2MILP represents MILP instances as bipartite graphs, and applies a masked variational autoencoder to iteratively corrupt and replace parts of the original graphs to generate new ones. The appealing feature of G2MILP is that it can learn to generate novel and realistic MILP instances without prior expert-designed formulations, while preserving the structures and computational hardness of real-world datasets, simultaneously. Thus the generated instances can facilitate downstream tasks for enhancing MILP solvers under limited data availability. We design a suite of benchmarks to evaluate the quality of the generated MILP instances. Experiments demonstrate that our method can produce instances that closely resemble real-world datasets in terms of both structures and computational hardness. The deliverables are released at [https://miralab-ustc.github.io/L2O-G2MILP](https://miralab-ustc.github.io/L2O-G2MILP).

This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms. Code is available at \url{https://github.com/xzhang2523/hvpsl/tree/master}.

Feature transformation aims to generate new pattern-discriminative feature space from original features to improve downstream machine learning (ML) task performances. However, the discrete search space for the optimal feature explosively grows on the basis of combinations of features and operations from low-order forms to high-order forms. Existing methods, such as exhaustive search, expansion reduction, evolutionary algorithms, reinforcement learning, and iterative greedy, suffer from large search space. Overly emphasizing efficiency in algorithm design usually sacrifice stability or robustness. To fundamentally fill this gap, we reformulate discrete feature transformation as a continuous space optimization task and develop an embedding-optimization-reconstruction framework. This framework includes four steps: 1) reinforcement-enhanced data preparation, aiming to prepare high-quality transformation-accuracy training data; 2) feature transformation operation sequence embedding, intending to encapsulate the knowledge of prepared training data within a continuous space; 3) gradient-steered optimal embedding search, dedicating to uncover potentially superior embeddings within the learned space; 4) transformation operation sequence reconstruction, striving to reproduce the feature transformation solution to pinpoint the optimal feature space. Finally, extensive experiments and case studies are performed to demonstrate the effectiveness and robustness of the proposed method. The code and data are publicly accessible https://www.dropbox.com/sh/imh8ckui7va3k5u/AACulQegVx0MuywYyoCqSdVPa?dl=0.

Optimizing proper loss functions is popularly believed to yield predictors with good calibration properties; the intuition being that for such losses, the global optimum is to predict the ground-truth probabilities, which is indeed calibrated. However, typical machine learning models are trained to approximately minimize loss over restricted families of predictors, that are unlikely to contain the ground truth. Under what circumstances does optimizing proper loss over a restricted family yield calibrated models? What precise calibration guarantees does it give? In this work, we provide a rigorous answer to these questions. We replace the global optimality with a local optimality condition stipulating that the (proper) loss of the predictor cannot be reduced much by post-processing its predictions with a certain family of Lipschitz functions. We show that any predictor with this local optimality satisfies smooth calibration as defined in [Kakade and Foster, 2008, Błasiok et al., 2023]. Local optimality is plausibly satisfied by well-trained DNNs, which suggests an explanation for why they are calibrated from proper loss minimization alone. Finally, we show that the connection between local optimality and calibration error goes both ways: nearly calibrated predictors are also nearly locally optimal.

We study the best arm identification problem in combinatorial semi-bandits in the fixed confidence setting. We present Perturbed Frank-Wolfe Sampling (P-FWS), an algorithm that (i) runs in polynomial time, (ii) achieves the instance-specific minimal sample complexity in the high confidence regime, and (iii) enjoys polynomial sample complexity guarantees in the moderate confidence regime. To our best knowledge, existing algorithms cannot achieve (ii) and (iii) simultaneously in vanilla bandits. With P-FWS, we close the computational-statistical gap in best arm identification in combinatorial semi-bandits. The design of P-FWS starts from the optimization problem that defines the information-theoretical and instance-specific sample complexity lower bound. P-FWS solves this problem in an online manner using, in each round, a single iteration of the Frank-Wolfe algorithm. Structural properties of the problem are leveraged to make the P-FWS successive updates computationally efficient. In turn, P-FWS only relies on a simple linear maximization oracle.

The differential equation (DE) approach for convex optimization, which relates optimization methods to specific continuous DEs with rate-revealing Lyapunov functionals, has gained increasing interest since the seminal paper by Su--Boyd--Candès (2014). However, the approach still lacks a crucial component to make it truly useful: there is no general, consistent way to transition back to discrete optimization methods. Consequently, even if we derive insights from continuous DEs, we still need to perform individualized and tedious calculations for the analysis of each method. This paper aims to bridge this gap by introducing a new concept called ``weak discrete gradient'' (wDG), which consolidates the conditions required for discrete versions of gradients in the DE approach arguments. We then define abstract optimization methods using wDG and provide abstract convergence theories that parallel those in continuous DEs. We demonstrate that many typical optimization methods and their convergence rates can be derived as special cases of this abstract theory. The proposed unified discretization framework for the differential equation approach to convex optimization provides an easy environment for developing new optimization methods and achieving competitive convergence rates with state-of-the-art methods, such as Nesterov's accelerated gradient.

This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimiza- tion problem, aiming to minimize the output prediction error. This formulation provides a direct bridge between data-driven optimal control and, its dual, op- timal filtering. Our contributions are twofold. Firstly, we conduct a thorough convergence analysis of the stochastic gradient descent algorithm, adopted for the filtering problem, accounting for biased gradients and stability constraints. Secondly, we carefully leverage a combination of tools from linear system theory and high-dimensional statistics to derive bias-variance error bounds that scale logarithmically with problem dimension, and, in contrast to subspace methods, the length of output trajectories only affects the bias term.

Experimental design is a fundamental problem in many science and engineering fields. In this problem, sample efficiency is crucial due to the time, money, and safety costs of real-world design evaluations. Existing approaches either rely on active data collection or access to large, labeled datasets of past experiments, making them impractical in many real-world scenarios. In this work, we address the more challenging yet realistic setting of few-shot experimental design, where only a few labeled data points of input designs and their corresponding values are available. We approach this problem as a conditional generation task, where a model conditions on a few labeled examples and the desired output to generate an optimal input design. To this end, we introduce Experiment Pretrained Transformers (ExPT), a foundation model for few-shot experimental design that employs a novel combination of synthetic pretraining with in-context learning. In ExPT, we only assume knowledge of a finite collection of unlabelled data points from the input domain and pretrain a transformer neural network to optimize diverse synthetic functions defined over this domain. Unsupervised pretraining allows ExPT to adapt to any design task at test time in an in-context fashion by conditioning on a few labeled data points from the target task and generating the candidate optima. We evaluate ExPT on few-shot experimental design in challenging domains and demonstrate its superior generality and performance compared to existing methods. The source code is available at https://github.com/tung-nd/ExPT.git.

Pandora’s Box is a central problem in decision making under uncertainty that can model various real life scenarios. In this problem we are given n boxes, each with a fixed opening cost, and an unknown value drawn from a known distribution, only revealed if we pay the opening cost. Our goal is to find a strategy for opening boxes to minimize the sum of the value selected and the opening cost paid. In this work we revisit Pandora’s Box when the value distributions are correlated, first studied in [CGT+20]. We show that the optimal algorithm for the independent case, given by Weitzman’s rule, directly works for the correlated case. In fact, our algorithm results in significantly improved approximation guarantees compared to the previous work, while also being substantially simpler. We also show how to implement the rule given only sample access to the correlated distribution of values. Specifically, we find that a number of samples that is polynomial in the number of boxes is sufficient for the algorithm to work.

We introduce the problem of Bayesian optimization with cost-varying variable subsets (BOCVS) where in each iteration, the learner chooses a subset of query variables and specifies their values while the rest are randomly sampled. Each chosen subset has an associated cost. This presents the learner with the novel challenge of balancing between choosing more informative subsets for more directed learning versus leaving some variables to be randomly sampled to reduce incurred costs. This paper presents a novel Gaussian process upper confidence bound-based algorithm for solving the BOCVS problem that is provably no-regret. We analyze how the availability of cheaper control sets helps in exploration and reduces overall regret. We empirically show that our proposed algorithm can find significantly better solutions than comparable baselines with the same budget.

The efficient frontier (EF) is a fundamental resource allocation problem where one has to find an optimal portfolio maximizing a reward at a given level of risk. This optimal solution is traditionally found by solving a convex optimization problem. In this paper, we introduce NeuralEF: a fast neural approximation framework that robustly forecasts the result of the EF convex optimizations problems with respect to heterogeneous linear constraints and variable number of optimization inputs. By reformulating an optimization problem as a sequence to sequence problem, we show that NeuralEF is a viable solution to accelerate large-scale simulation while handling discontinuous behavior.

This study reveals the inherent tolerance of contrastive learning (CL) towards sampling bias, wherein negative samples may encompass similar semantics (\eg labels). However, existing theories fall short in providing explanations for this phenomenon. We bridge this research gap by analyzing CL through the lens of distributionally robust optimization (DRO), yielding several key insights: (1) CL essentially conducts DRO over the negative sampling distribution, thus enabling robust performance across a variety of potential distributions and demonstrating robustness to sampling bias; (2) The design of the temperature $\tau$ is not merely heuristic but acts as a Lagrange Coefficient, regulating the size of the potential distribution set; (3) A theoretical connection is established between DRO and mutual information, thus presenting fresh evidence for ``InfoNCE as an estimate of MI'' and a new estimation approach for $\phi$-divergence-based generalized mutual information. We also identify CL's potential shortcomings, including over-conservatism and sensitivity to outliers, and introduce a novel Adjusted InfoNCE loss (ADNCE) to mitigate these issues. It refines potential distribution, improving performance and accelerating convergence. Extensive experiments on various domains (image, sentence, and graph) validate the effectiveness of the proposal.

Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MOCOPs). However, they are still struggling to achieve high learning efficiency and solution quality. To tackle this issue, we propose an efficient meta neural heuristic (EMNH), in which a meta-model is first trained and then fine-tuned with a few steps to solve corresponding single-objective subproblems. Specifically, for the training process, a (partial) architecture-shared multi-task model is leveraged to achieve parallel learning for the meta-model, so as to speed up the training; meanwhile, a scaled symmetric sampling method with respect to the weight vectors is designed to stabilize the training. For the fine-tuning process, an efficient hierarchical method is proposed to systematically tackle all the subproblems. Experimental results on the multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) show that, EMNH is able to outperform the state-of-the-art neural heuristics in terms of solution quality and learning efficiency, and yield competitive solutions to the strong traditional heuristics while consuming much shorter time.

Hyperparameter optimization, also known as hyperparameter tuning, is a widely recognized technique for improving model performance. Regrettably, when training private ML models, many practitioners often overlook the privacy risks associated with hyperparameter optimization, which could potentially expose sensitive information about the underlying dataset. Currently, the sole existing approach to allow privacy-preserving hyperparameter optimization is to uniformly and randomly select hyperparameters for a number of runs, subsequently reporting the best-performing hyperparameter. In contrast, in non-private settings, practitioners commonly utilize "adaptive" hyperparameter optimization methods such as Gaussian Process-based optimization, which select the next candidate based on information gathered from previous outputs. This substantial contrast between private and non-private hyperparameter optimization underscores a critical concern. In our paper, we introduce DP-HyPO, a pioneering framework for "adaptive" private hyperparameter optimization, aiming to bridge the gap between private and non-private hyperparameter optimization. To accomplish this, we provide a comprehensive differential privacy analysis of our framework. Furthermore, we empirically demonstrate the effectiveness of DP-HyPO on a diverse set of real-world datasets.

This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a differential Karush-Kuhn-Tucker (KKT) system for the trajectory derivative, and achieve this efficiently by solving an auxiliary Linear Quadratic Regulator (LQR) problem. In contrast, we directly evaluate the matrix equations which arise from applying variable elimination on the Lagrange multiplier terms in the (differential) KKT system. By appropriately accounting for the structure of the terms within the resulting equations, we show that the trajectory derivatives scale linearly with the number of timesteps. Furthermore, our approach allows for easy parallelization, significantly improved scalability with model size, direct computation of vector-Jacobian products and improved numerical stability compared to prior works. As an additional contribution, we unify prior works, addressing claims that computing trajectory derivatives using IFT scales quadratically with the number of timesteps. We evaluate our method on a both synthetic benchmark and four challenging, learning from demonstration benchmarks including a 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.

This paper proposes a new easy-to-implement parameter-free gradient-based optimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG is efficient---matching the convergence rate of optimally tuned gradient descent in convex optimization up to a logarithmic factor without tuning any parameters, and universal---automatically adapting to both smooth and nonsmooth problems. While popular algorithms following the AdaGrad framework compute a running average of the squared gradients, DoWG maintains a new distance-based weighted version of the running average, which is crucial to achieve the desired properties. To complement our theory, we also show empirically that DoWG trains at the edge of stability, and validate its effectiveness on practical machine learning tasks.

One of the most popular ML algorithms, AdaBoost, can be derived from the dual of a relative entropy minimization problem subject to the fact that the positive weights on the examples sum to one. Essentially, harder examples receive higher probabilities. We generalize this setup to the recently introduced *tempered exponential measure*s (TEMs) where normalization is enforced on a specific power of the measure and not the measure itself. TEMs are indexed by a parameter $t$ and generalize exponential families ($t=1$). Our algorithm, $t$-AdaBoost, recovers AdaBoost as a special case ($t=1$). We show that $t$-AdaBoost retains AdaBoost's celebrated exponential convergence rate when $t\in [0,1)$ while allowing a slight improvement of the rate's hidden constant compared to $t=1$. $t$-AdaBoost partially computes on a generalization of classical arithmetic over the reals and brings notable properties like guaranteed bounded leveraging coefficients for $t\in [0,1)$. From the loss that $t$-AdaBoost minimizes (a generalization of the exponential loss), we show how to derive a new family of *tempered* losses for the induction of domain-partitioning classifiers like decision trees. Crucially, strict properness is ensured for all while their boosting rates span the full known spectrum. Experiments using $t$-AdaBoost+trees display that significant leverage can be achieved by tuning $t$.

Online convex optimization (OCO) is a widely used framework in online learning. In each round, the learner chooses a decision in a convex set and an adversary chooses a convex loss function, and then the learner suffers the loss associated with their current decision. However, in many applications the learner's loss depends not only on the current decision but on the entire history of decisions until that point. The OCO framework and its existing generalizations do not capture this, and they can only be applied to many settings of interest after a long series of approximation arguments. They also leave open the question of whether the dependence on memory is tight because there are no non-trivial lower bounds. In this work we introduce a generalization of the OCO framework, ``Online Convex Optimization with Unbounded Memory'', that captures long-term dependence on past decisions. We introduce the notion of $p$-effective memory capacity, $H_p$, that quantifies the maximum influence of past decisions on present losses. We prove an $O(\sqrt{H_p T})$ upper bound on the policy regret and a matching (worst-case) lower bound. As a special case, we prove the first non-trivial lower bound for OCO with finite memory~\citep{anavaHM2015online}, which could be of independent interest, and also improve existing upper bounds. We demonstrate the broad applicability of our framework by using it to derive regret bounds, and to improve and simplify existing regret bound derivations, for a variety of online learning problems including online linear control and an online variant of performative prediction.