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Minh-Duc Nguyen, Phuong Mai Dinh, Quang-Huy Nguyen, Long P. Hoang, Dung D. Le

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

Mohammadreza Nakhaeinezhadfard, Aidan Scannell, Joni Pajarinen

Offline meta-reinforcement learning aims to equip agents with the ability to rapidly adapt to new tasks by training on data from a set of different tasks. Context-based approaches utilize a history of state-action-reward transitions – referred to as the context – to infer a representation of the current task, and then condition the agent, i.e., the policy and value function, on this task representation. Intuitively, the better the task representation captures the underlying tasks, the better the agent can generalize to new tasks. Unfortunately, context-based approaches suffer from distribution mismatch, as the context in the offline data does not match the context at test time, limiting their ability to generalize to the test task. This leads to the task representation overfitting to the offline training data. Intuitively, the task representation should be independent of the behavior policy used to collect the offline data. To address this issue, we approximately minimize the mutual information between the distribution over the task representation and behavior policy by maximizing the entropy of behavior policy conditioned on the task representation. We validate our approach in MuJoCo environments, showing that compared to baselines, our task representation more faithfully represents the underlying tasks, leading to outperforming prior methods in both in-distribution and out-of-distribution tasks.

Xin Li, Chengli Zhao, Xue Zhang, Xiaojun Duan

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great significance. In this study, we propose a novel learning framework of symbolic continuous-depth neural networks, termed Symbolic Neural Ordinary Differential Equations (SNODEs), to effectively and accurately learn the underlying dynamics of complex systems. Specifically, our learning framework comprises three stages: initially, pre-training a predefined symbolic neural network via a gradient flow matching strategy; subsequently, fine-tuning this network using Neural ODEs; and finally, constructing a general neural network to capture residuals. In this process, we apply the SNODEs framework to partial differential equation systems through Fourier analysis, achieving resolution-invariant modeling. Moreover, this framework integrates the strengths of symbolism and connectionism, boasting a universal approximation theorem while significantly enhancing interpretability and extrapolation capabilities relative to state-of-the-art baseline methods. We demonstrate this through experiments on several representative complex systems. Therefore, our framework can be further applied to a wide range of scientific problems, such as system bifurcation and control, reconstruction and forecasting, as well as the discovery of new equations.

Feijiang Li, Jieting Wang, Liuya Zhang, Yuhua Qian, Shuai Jin, Tao Yan, Liang Du

Clustering ensemble has been a popular research topic in data science due to its ability to improve the robustness of the single clustering method. Many clustering ensemble methods have been proposed, most of which can be categorized into clustering-view and sample-view methods. The clustering-view method is generally efficient, but it could be affected by the unreliability that existed in base clustering results. The sample-view method shows good performance, while the construction of the pairwise sample relation is time-consuming. In this paper, the clustering ensemble is formulated as a k-HyperEdge Medoids discovery problem and a clustering ensemble method based on k-HyperEdge Medoids that considers the characteristics of the above two types of clustering ensemble methods is proposed. In the method, a set of hyperedges is selected from the clustering view efficiently, then the hyperedges are diffused and adjusted from the sample view guided by a hyperedge loss function to construct an effective k-HyperEdge Medoid set. The loss function is mainly reduced by assigning samples to the hyperedge with the highest degree of belonging. Theoretical analyses show that the solution can approximate the optimal, the assignment method can gradually reduce the loss function, and the estimation of the belonging degree is statistically reasonable. Experiments on artificial data show the working mechanism of the proposed method. The convergence of the method is verified by experimental analysis of twenty data sets. The effectiveness and efficiency of the proposed method are also verified on these data, with nine representative clustering ensemble algorithms as reference.

Minyoung Kim, Timothy Hospedales

We tackle the general differentiable meta learning problem that is ubiquitous in modern deep learning, including hyperparameter optimization, loss function learning, few-shot learning and more. These problems are often formalized as Bi-Level Optimizations (BLO). We introduce a novel perspective by turning a given BLO problem into a stochastic optimization, where the inner loss function becomes a smooth probability distribution, and the outer loss becomes an expected loss over the inner distribution. To solve this stochastic optimization, we adopt Stochastic Gradient Langevin Dynamics (SGLD) MCMC to sample inner distribution, and propose a recurrent algorithm to compute the MC-estimated hypergradient. Our derivation is similar to forward-mode differentiation, but we introduce a new first-order approximation that makes it feasible for large models without needing to store huge Jacobian matrices. The main benefits are two fold: i) Our stochastic formulation takes into account uncertainty, which makes the method robust to suboptimal inner optimization or non-unique multiple inner minima due to overparametrization; ii) Compared to existing methods that often exhibit unstable behavior and hyperparameter sensitivity in practice, our method leads to considerably more reliable solutions. We demonstrate that the new approach achieves promising results on diverse meta learning problems and easily scales to learning 87M hyper-parameters in the case of Vision Transformers.

Xiaoyu Hu, Zhenhua Lin

Posterior drift refers to changes in the relationship between responses and covariates while the distributions of the covariates remain unchanged. In this work, we explore functional linear regression under posterior drift with transfer learning. Specifically, we investigate when and how auxiliary data can be leveraged to improve the estimation accuracy of the slope function in the target model when posterior drift occurs. We employ the approximated least square method together with a lasso penalty to construct an estimator that transfers beneficial knowledge from source data. Theoretical analysis indicates that our method avoids negative transfer under posterior drift, even when the contrast between slope functions is quite large. Specifically, the estimator is shown to perform at least as well as the classical estimator using only target data, and it enhances the learning of the target model when the source and target models are sufficiently similar. Furthermore, to address scenarios where covariate distributions may change, we propose an adaptive algorithm using aggregation techniques. This algorithm is robust against non-informative source samples and effectively prevents negative transfer. Simulation and real data examples are provided to demonstrate the effectiveness of the proposed algorithm.

Xingcheng Fu, Jian Wang, Yisen Gao, Qingyun Sun, Haonan Yuan, Jianxin Li, Xianxian Li

Graph neural networks(GNNs) have been demonstrated to depend on whether the node effective information is sufficiently passing. Discrete curvature (Ricci curvature) is used to study graph connectivity and information propagation efficiency with a geometric perspective, and has been raised in recent years to explore the efficient message-passing structure of GNNs. However, most empirical studies are based on directly observed graph structures or heuristic topological assumptions, and lack in-depth exploration of underlying optimal information transport structures for downstream tasks. We suggest that graph curvature optimization is more in-depth and essential than directly rewiring or learning for graph structure with richer message-passing characterization and better information transport interpretability. From both graph geometry and information theory perspectives, we propose the novel Discrete Curvature Graph Information Bottleneck (CurvGIB) framework to optimize the information transport structure and learn better node representations simultaneously. CurvGIB advances the Variational Information Bottleneck (VIB) principle for Ricci curvature optimization to learn the optimal information transport pattern for specific downstream tasks. The learned Ricci curvature is used to refine the optimal transport structure of the graph, and the node representation is fully and efficiently learned. Moreover, for the computational complexity of Ricci curvature differentiation, we combine Ricci flow and VIB to deduce a curvature optimization approximation to form a tractable IB objective function. Extensive experiments on various datasets demonstrate the superior effectiveness and interpretability of CurvGIB.

Songtao Feng, Michael Dorothy, Jie Fu

The problem of constrained Markov game has recently attracted interests in the study of multi-agent reinforcement learning (MARL). The existing literature has focused on safe MARL problems where safety constraints are imposed for each agent individually. In this work, we consider Markov potential game (MPG) with a shared constraint, where the cost function with respect to the constraint depends on states and joint actions of all agents. We adopt a primal-dual framework to tackle the problem and establish the Slater condition to ensure the strong duality. Moreover, we propose our primal-dual learning algorithm for learning approximate Nash equilibrium in MPG with shared constraint. Thanks to the novel design of the dual update, we provide asymptotic convergence on the weighted output policy. Specifically, we prove that both the value function gap and the constraint violation of the output policy converge at the rate O(epsilon+1/sqrt(T)), where epsilon is the accuracy level of the primal update, and T is the number of iterations. We further show that the weighted output policy outperforms the existing uniformly chosen policy.

Chen Dun, Mirian Del Carmen Hipolito Garcia, Guoqing Zheng, Ahmed Hassan Awadallah, Robert Sim, Anastasios Kyrillidis

Prompt instruction tuning is a popular approach to better adjust pretrained LLMs for specific downstream tasks. How to extend this approach to simultaneously handle multiple tasks and data distributions is an interesting question. We propose Mixture of Prompts (MoPs) with smart gating functionality. Our proposed system identifies relevant skills embedded in different groups of prompts and dynamically weighs experts (i.e., collection of prompts) based on the target task. Experiments show that MoPs are resilient to model compression, data source, and task composition, making them highly versatile and applicable in various contexts. In practice, MoPs can simultaneously mitigate prompt training ``interference'' in multi-task, multi-source scenarios (e.g., task and data heterogeneity across sources) and possible implications from model approximations. Empirically, MoPs show particular effectiveness in compressed model scenarios, while maintaining favorable performance in uncompressed settings: MoPs can reduce final perplexity from 9% up to 70% in non-i.i.d. distributed cases and from 3% up to 30% in centralized cases, compared to baselines.

Wenjun Ding, Ying An, Lixing Chen, Shichao Kan, Fan Wu, Zhe Qu

Federated Adversarial Learning (FAL) is a robust framework for resisting adversarial attacks on federated learning. Although some FAL studies have developed efficient algorithms, they primarily focus on convergence performance and overlook generalization. Generalization is crucial for evaluating algorithm performance on unseen data. However, generalization analysis is more challenging due to non-smooth adversarial loss functions. A common approach to addressing this issue is to leverage smoothness approximation. In this paper, we develop algorithm stability measures to evaluate the generalization performance of two popular FAL algorithms: Vanilla FAL (VFAL) and Slack FAL (SFAL), using three different smooth approximation methods: 1) Surrogate Smoothness Approximation (SSA), (2) Randomized Smoothness Approximation (RSA), and (3) Over-Parameterized Smoothness Approximation (OPSA). Based on our in-depth analysis, we answer how to properly set the smoothness approximation method to mitigate generalization error in FAL. Moreover, we identify RSA as the most effective generalization error reduction method. In highly data-heterogeneous scenarios, we also recommend employing SFAL to mitigate the deterioration of generalization performance caused by heterogeneity. Based on our theoretical results, we provide insights to help develop more efficient FAL algorithms, such as designing new metrics and dynamic aggregation rules to mitigate heterogeneity.

Jingda Deng, Jianyong Sun, Qingfu Zhang, Hui Li

Multi-objective Bayesian optimization (MOBO) aims to optimize multiple competing objective functions in the expensive-to-evaluate scenario. The Expected Hypervolume Improvement (EHVI) is a commonly used acquisition function for MOBO and shows a good performance. However, the computation of EHVI becomes challenging as the number of objective functions grows. In this paper, we revisit the formulation of EHVI, as well as its multi-point counterpart qEHVI, and derive much simpler analytic expressions for them. The main contributions of this paper include: (1) first formulating EHVI as a particular hypervolume improvement, and thus immediately obtaining a formal proof of its NP-hardness, faster algorithms in both theory and practice, and more results on its derivatives; (2) first obtaining the analytic expressions of qEHVI for any q > 1 and m ≥ 2 where m is the number of objectives; and (3) demonstrating the advantages of our formulation over existing exact and approximation methods for computing EHVI and qEHVI through a large number of numerical experiments.

Zixi Chen, Yumin Xu, Ruixun Zhang

The nonlinear two-time-scale stochastic approximation is widely studied under conditions of bounded variances in noise. Motivated by recent advances that allow for variability linked to the current state or time, we consider state- and time-dependent noises. We show that the Lyapunov function exhibits polynomial convergence rates in both cases, with the rate of polynomial delay depending on the parameters of state- or time-dependent noises. Notably, if the state noise parameters fully approach their limiting value, the Lyapunov function achieves an exponential convergence rate. We provide two numerical examples to illustrate our theoretical findings in the context of stochastic gradient descent with Polyak-Ruppert averaging and stochastic bilevel optimization.

Afrad Basheer, Yuan Feng, Christopher Ferrie, Sanjiang Li, Hakop Pashayan

We prove that using global observables to train the matrix product state ansatz results in the vanishing of all partial derivatives, also known as barren plateaus, while using local observables avoids this. This ansatz is widely used in quantum machine learning for learning weakly entangled state approximations. Additionally, we empirically demonstrate that in many cases, the objective function is an inner product of almost sparse operators, highlighting the potential for classically simulating such a learning problem with few quantum resources. All our results are experimentally validated across various scenarios.

Mateus De Oliveira Oliveira

Equational reasoning is one of the most intuitive and widely used types of symbolic reasoning. In this setting, the goal is to determine whether a given ground equation t=t' follows as a consequence of a set of equational axioms E using the process of replacing equals with equals. An equation t=t' is variable-preserving if each variable occurring in t occurs in t' and vice versa. Such equations capture essential algebraic properties, such as commutativity, associativity and distributivity, which arise in a wide variety of contexts. In this work, we show that for each fixed set E of variable-preserving equations, the set of ground equations derivable from E in depth at most d is soundly over-approximable in fixed-parameter tractable time. More specifically, we devise an algorithm that takes as input a set E of variable-preserving equations and a target ground equation t=t', and always halts with a YES or NO answer. 1) If equation t=t' can be derived from E in depth at most d, the algorithm always halts with a YES. 2) If equation t=t' does not belong to the equational closure of E, then the algorithm always halts with a NO. In other words, the set of YES instances contains the set of ground equations that can be deduced from E in depth at most d, and possibly other equations that require derivations of higher depth. However, this set contains no ground equation that is not in the equational closure of E. For this reason, the algorithm is sound. Our algorithm works in time f(d) * |t| * |t'|, where |t| and |t'| are the number of symbols in t and t' respectively, d is the depth parameter, and f(d) is a function whose growth depends only on d and on parameters associated with the equations in E.

Mingquan Feng, Zhijie Chen, Yixin Huang, Yizhou Liu, Junchi Yan

Optimal control problems (OCPs) involve finding a control function for a dynamical system such that a cost functional is optimized. It is central to physical systems in both academia and industry. In this paper, we propose a novel instance-solution control operator perspective, which solves OCPs in a one-shot manner without direct dependence on the explicit expression of dynamics or iterative optimization processes. The control operator is implemented by a new neural operator architecture named Neural Adaptive Spectral Method (NASM), a generalization of classical spectral methods. We theoretically validate the perspective and architecture by presenting the approximation error bounds of NASM for the control operator. Experiments on synthetic environments and a real-world dataset verify the effectiveness and efficiency of our approach, including substantial speedup in running time, and high-quality in- and out-of-distribution generalization.

Yinxu Tang, Stylianos Loukas Vasileiou, William Yeoh

Explainable AI is increasingly employing argumentation methods to facilitate interactive explanations between AI agents and human users. While existing approaches typically rely on predetermined human user models, there remains a critical gap in dynamically learning and updating these models during interactions. In this paper, we present a framework that enables AI agents to adapt their understanding of human users through argumentation-based dialogues. Our approach, called Persona, draws on prospect theory and integrates a probability weighting function with a Bayesian belief update mechanism that refines a probability distribution over possible human models based on exchanged arguments. Through empirical evaluations with human users in an applied argumentation setting, we demonstrate that Persona effectively captures evolving human beliefs, facilitates personalized interactions, and outperforms state-of-the-art methods.

Lulu Cao, Zexin Lin, Kay Chen Tan, Min Jiang

Multiphysics simulation aims to predict and understand interactions between multiple physical phenomena, aiding in comprehending natural processes and guiding engineering design. The system of Partial Differential Equations (PDEs) is crucial for representing these physical fields, and solving these PDEs is fundamental to such simulations. However, current methods primarily yield numerical outputs, limiting interpretability and generalizability. We introduce T-NNGP, a hybrid genetic programming algorithm that integrates traditional numerical methods with deep learning to derive approximate symbolic expressions for multiple unknown functions within a system of PDEs. T-NNGP initially obtains numerical solutions using traditional methods, then generates candidate symbolic expressions via deep reinforcement learning, and finally optimizes these expressions using genetic programming. Furthermore, a universal decoupling strategy guides the search direction and addresses coupling problems, thereby accelerating the search process. Experimental results on three types of PDEs demonstrate that our method can reliably obtain human-understandable symbolic expressions that fit both the PDEs and the numerical solutions from traditional methods. This work advances multiphysics simulation by enhancing our ability to derive approximate symbolic solutions for PDEs, thereby improving our understanding of complex physical phenomena.

Jugal Garg, Xin Huang, Erel Segal-Halevi

We study fair division of indivisible chores among n agents with additive cost functions using the popular fairness notion of maximin share (MMS). Since MMS allocations do not always exist for more than two agents, the goal has been to improve its approximations and identify interesting special cases where MMS allocations exist. We show the existence of · 1-out-of-9n/11 MMS allocations, which improves the state-of-the-art factor of 1-out-of-3n/4. · MMS allocations for factored instances, which resolves an open question posed by Ebadian et al. (2021). · 15/13-MMS allocations for personalized bivalued instances, improving the state-of-the-art factor of 13/11. We achieve these results by leveraging the HFFD algorithm of Huang and Lu (2021). Our approach also provides polynomial-time algorithms for computing an MMS allocation for factored instances and a 15/13-MMS allocation for personalized bivalued instances.

Michele Flammini, Gianluigi Greco, Giovanna Varricchio

In this paper, we consider the problem of fair division of indivisible goods, where the allocation of goods impacts society. Specifically, we introduce a second valuation function for each agent, which determines the social impact of allocating a good to the agent. Such impact is considered desirable for the society -- the higher, the better. Our goal is to understand how to allocate goods fairly from the agents' perspective while maintaining society as happy as possible. To this end, we measure the impact on society using the utilitarian social welfare, and provide both possibility and impossibility results. Our findings reveal that achieving good approximations, better than linear in the number of agents, is not possible while ensuring fairness to the agents. These impossibility results can be attributed to the fact that agents are completely unconscious of their social impact. Consequently, we explore scenarios where agents are socially aware, by introducing related fairness notions, and demonstrate that an appropriate definition of fairness is compatible with the social objective.

Michal Feldman, Jugal Garg, Vishnu V. Narayan, Tomasz Ponitka

We study fair mechanisms for the classic job scheduling problem on unrelated machines with the objective of minimizing the makespan. This problem is equivalent to minimizing the egalitarian social cost in the fair division of chores. The two prevalent fairness notions in the fair division literature are envy-freeness and proportionality. Prior work has established that no envy-free mechanism can provide better than an Ω(log m / log log m)-approximation to the optimal makespan, where m is the number of machines, even when payments to the machines are allowed. In strong contrast to this impossibility, our main result demonstrates that there exists a proportional mechanism (with payments) that achieves a 3/2-approximation to the optimal makespan, and this ratio is tight. To prove this result, we provide a full characterization of allocation functions that can be made proportional with payments. Furthermore, we show that for instances with normalized costs, there exists a proportional mechanism that achieves the optimal makespan. We conclude with important directions for future research concerning other fairness notions, including relaxations of envy-freeness. Notably, we show that the technique leading to the impossibility result for envy-freeness does not extend to its relaxations.