Offline Model-Based Optimization by Learning to Rank

Offline model-based optimization (MBO) aims to identify a design that maximizes a black-box function using only a fixed, pre-collected dataset of designs and their corresponding scores. A common approach in offline MBO is to train a regression-based surrogate model by minimizing mean squared error (MSE) and then find the best design within this surrogate model by different optimizers (e.g., gradient ascent). However, a critical challenge is the risk of out-of-distribution errors, i.e., the surrogate model may typically overestimate the scores and mislead the optimizers into suboptimal regions. Prior works have attempted to address this issue in various ways, such as using regularization techniques and ensemble learning to enhance the robustness of the model, but it still remains. In this paper, we argue that regression models trained with MSE are not well-aligned with the primary goal of offline MBO, which is to select promising designs rather than to predict their scores precisely. Notably, if a surrogate model can maintain the order of candidate designs based on their relative score relationships, it can produce the best designs even without precise predictions. To validate it, we conduct experiments to compare the relationship between the quality of the final designs and MSE, finding that the correlation is really very weak. In contrast, a metric that measures order-maintaining quality shows a significantly stronger correlation. Based on this observation, we propose learning a ranking-based model that leverages learning to rank techniques to prioritize promising designs based on their relative scores. We show that the generalization error on ranking loss can be well bounded. Empirical results across diverse tasks demonstrate the superior performance of our proposed ranking-based models than twenty existing methods.

Neural Solver Selection for Combinatorial Optimization

Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To date, the community has created numerous open-source neural solvers with distinct motivations and inductive biases. While considerable efforts are devoted to designing powerful single solvers, our findings reveal that existing solvers typically demonstrate complementary performance across different problem instances. This suggests that significant improvements could be achieved through effective coordination of neural solvers at the instance level. In this work, we propose the first general framework to coordinate the neural solvers, which involves feature extraction, selection model, and selection strategy, aiming to allocate each instance to the most suitable solvers. To instantiate, we collect several typical neural solvers with state-of-the-art performance as alternatives, and explore various methods for each component of the framework. We evaluated our framework on two extensively studied combinatorial optimization problems, Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP). Experimental results show that the proposed framework can effectively distribute instances and the resulting composite solver can achieve significantly better performance (e.g., reduce the optimality gap by 0.88\% on TSPLIB and 0.71\% on CVRPLIB) than the best individual neural solver with little extra time cost.

Offline Multi-Objective Optimization

Offline optimization aims to maximize a black-box objective function with a static dataset and has wide applications. In addition to the objective function being black-box and expensive to evaluate, numerous complex real-world problems entail optimizing multiple conflicting objectives, i.e., multi-objective optimization (MOO). Nevertheless, offline MOO has not progressed as much as offline single-objective optimization (SOO), mainly due to the lack of benchmarks like Design-Bench for SOO. To bridge this gap, we propose a first benchmark for offline MOO, covering a range of problems from synthetic to real-world tasks. This benchmark provides tasks, datasets, and open-source examples, which can serve as a foundation for method comparisons and advancements in offline MOO. Furthermore, we analyze how the current related methods can be adapted to offline MOO from four fundamental perspectives, including data, model architecture, learning algorithm, and search algorithm. Empirical results show improvements over the best value of the training set, demonstrating the effectiveness of offline MOO methods. As no particular method stands out significantly, there is still an open challenge in further enhancing the effectiveness of offline MOO. We finally discuss future challenges for offline MOO, with the hope of shedding some light on this emerging field. Our code is available at \url{https://github.com/lamda-bbo/offline-moo}.

Quality-Diversity with Limited Resources

Quality-Diversity (QD) algorithms have emerged as a powerful optimization paradigm with the aim of generating a set of high-quality and diverse solutions. To achieve such a challenging goal, QD algorithms require maintaining a large archive and a large population in each iteration, which brings two main issues, sample and resource efficiency. Most advanced QD algorithms focus on improving the sample efficiency, while the resource efficiency is overlooked to some extent. Particularly, the resource overhead during the training process has not been touched yet, hindering the wider application of QD algorithms. In this paper, we highlight this important research question, i.e., how to efficiently train QD algorithms with limited resources, and propose a novel and effective method called RefQD to address it. RefQD decomposes a neural network into representation and decision parts, and shares the representation part with all decision parts in the archive to reduce the resource overhead. It also employs a series of strategies to address the mismatch issue between the old decision parts and the newly updated representation part. Experiments on different types of tasks from small to large resource consumption demonstrate the excellent performance of RefQD: it not only uses significantly fewer resources (e.g., 16\% GPU memories on QDax and 3.7\% on Atari) but also achieves comparable or better performance compared to sample-efficient QD algorithms. Our code is available at \url{https://github.com/lamda-bbo/RefQD}.

Escaping Local Optima in Global Placement

Placement is crucial in the physical design, as it greatly affects power, performance, and area metrics. Recent advancements in analytical methods, such as DREAMPlace, have demonstrated impressive performance in global placement. However, DREAMPlace has some limitations, e.g., may not guarantee legalizable placements under the same settings, leading to fragile and unpredictable results. This paper highlights the main issue as being stuck in local optima, and proposes a hybrid optimization framework to efficiently escape the local optima, by perturbing the placement result iteratively. The proposed framework achieves significant improvements compared to state-of-the-art methods on two popular benchmarks.

Reinforced In-Context Black-Box Optimization

Black-Box Optimization (BBO) has found successful applications in many fields of science and engineering. Recently, there has been a growing interest in meta-learning particular components of BBO algorithms to speed up optimization and get rid of tedious hand-crafted heuristics. As an extension, learning the entire algorithm from data requires the least labor from experts and can provide the most flexibility. In this paper, we propose RIBBO, a method to reinforce-learn a BBO algorithm from offline data in an end-to-end fashion. RIBBO employs expressive sequence models to learn the optimization histories produced by multiple behavior algorithms and tasks, leveraging the in-context learning ability of large models to extract task information and make decisions accordingly. Central to our method is to augment the optimization histories with regret-to-go tokens, which are designed to represent the performance of an algorithm based on cumulative regret of the histories. The integration of regret-to-go tokens enables RIBBO to automatically generate sequences of query points that satisfy the user-desired regret, which is verified by its universally good empirical performance on diverse problems, including BBOB functions, hyper-parameter optimization and robot control problems.

Quality-Diversity Algorithms Can Provably Be Helpful for Optimization

Quality-Diversity (QD) algorithms are a new type of Evolutionary Algorithms (EAs), aiming to find a set of high-performing, yet diverse solutions. They have found many successful applications in reinforcement learning and robotics, helping improve the robustness in complex environments. Furthermore, they often empirically find a better overall solution than traditional search algorithms which explicitly search for a single highest-performing solution. However, their theoretical analysis is far behind, leaving many fundamental questions unexplored. In this paper, we try to shed some light on the optimization ability of QD algorithms via rigorous running time analysis. By comparing the popular QD algorithm MAP-Elites with $(\mu+1)$-EA (a typical EA focusing on finding better objective values only), we prove that on two NP-hard problem classes with wide applications, i.e., monotone approximately submodular maximization with a size constraint, and set cover, MAP-Elites can achieve the (asymptotically) optimal polynomial-time approximation ratio, while $(\mu+1)$-EA requires exponential expected time on some instances. This provides theoretical justification for that QD algorithms can be helpful for optimization, and discloses that the simultaneous search for high-performing solutions with diverse behaviors can provide stepping stones to good overall solutions and help avoid local optima.

Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation

Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.

Diversity from Human Feedback

Diversity plays a significant role in many problems, such as ensemble learning, reinforcement learning, and combinatorial optimization. How to define the diversity measure is a longstanding problem. Many methods rely on expert experience to define a proper behavior space and then obtain the diversity measure, which is, however, challenging in many scenarios. In this paper, we propose the problem of learning a behavior space from human feedback and present a general method called Diversity from Human Feedback (DivHF) to solve it. DivHF learns a behavior descriptor consistent with human preference by querying human feedback. The learned behavior descriptor can be combined with any distance measure to define a diversity measure. We demonstrate the effectiveness of DivHF by integrating it with the Quality-Diversity optimization algorithm MAP-Elites and conducting experiments on the QDax suite. The results show that DivHF learns a behavior space that aligns better with human requirements compared to direct data-driven approaches and leads to more diverse solutions under human preference. Our contributions include formulating the problem, proposing the DivHF method, and demonstrating its effectiveness through experiments.

Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy

Machine learning has been adapted to help solve NP-hard combinatorial optimization problems. One prevalent way is learning to construct solutions by deep neural networks, which has been receiving more and more attention due to the high efficiency and less requirement for expert knowledge. However, many neural construction methods for Vehicle Routing Problems (VRPs) focus on synthetic problem instances with limited scales and specified node distributions, leading to poor performance on real-world problems which usually involve large scales together with complex and unknown node distributions. To make neural VRP solvers more practical in real-world scenarios, we design an auxiliary policy that learns from the local transferable topological features, named local policy, and integrate it with a typical constructive policy (which learns from the global information of VRP instances) to form an ensemble policy. With joint training, the aggregated policies perform cooperatively and complementarily to boost generalization. The experimental results on two well-known benchmarks, TSPLIB and CVRPLIB, of travelling salesman problem and capacitated VRP show that the ensemble policy consistently achieves better generalization than state-of-the-art construction methods and even works well on real-world problems with several thousand nodes.