In bandit best-arm identification, an algorithm is tasked with finding the arm with highest mean reward with a specified accuracy as fast as possible. We study multi-fidelity best-arm identification, in which the algorithm can choose to sample an arm at a lower fidelity (less accurate mean estimate) for a lower cost. Several methods have been proposed for tackling this problem, but their optimality remain elusive, notably due to loose lower bounds on the total cost needed to identify the best arm. Our first contribution is a tight, instance-dependent lower bound on the cost complexity. The study of the optimization problem featured in the lower bound provides new insights to devise computationally efficient algorithms, and leads us to propose a gradient-based approach with asymptotically optimal cost complexity. We demonstrate the benefits of the new algorithm compared to existing methods in experiments. Our theoretical and empirical findings also shed light on an intriguing concept of optimal fidelity for each arm.

We consider the problem of sequentially maximizing an unknown function $f$ over a set of actions of the form $(s,\mathbf{x})$, where the selected actions must satisfy a safety constraint with respect to an unknown safety function $g$. We model $f$ and $g$ as lying in a reproducing kernel Hilbert space (RKHS), which facilitates the use of Gaussian process methods. While existing works for this setting have provided algorithms that are guaranteed to identify a near-optimal safe action, the problem of attaining low cumulative regret has remained largely unexplored, with a key challenge being that expanding the safe region can incur high regret. To address this challenge, we show that if $g$ is monotone with respect to just the single variable $s$ (with no such constraint on $f$), sublinear regret becomes achievable with our proposed algorithm. In addition, we show that a modified version of our algorithm is able to attain sublinear regret (for suitably defined notions of regret) for the task of finding a near-optimal $s$ corresponding to every $\mathbf{x}$, as opposed to only finding the global safe optimum. Our findings are supported with empirical evaluations on various objective and safety functions.

In recent years, interest in gradient-based optimization over Riemannian manifolds has surged. However, a significant challenge lies in the reliance on hyperparameters, especially the learning rate, which requires meticulous tuning by practitioners to ensure convergence at a suitable rate. In this work, we introduce innovative learning-rate-free algorithms for stochastic optimization over Riemannian manifolds, eliminating the need for hand-tuning and providing a more robust and user-friendly approach. We establish high probability convergence guarantees that are optimal, up to logarithmic factors, compared to the best-known optimally tuned rate in the deterministic setting. Our approach is validated through numerical experiments, demonstrating competitive performance against learning-rate-dependent algorithms.

Recent years have seen a growing interest in understanding acceleration methods through the lens of ordinary differential equations (ODEs). Despite the theoretical advancements, translating the rapid convergence observed in continuous-time models to discrete-time iterative methods poses significant challenges. In this paper, we present a comprehensive framework integrating the inertial systems with Hessian-driven damping equation (ISHD) and learning-based approaches for developing optimization methods through a deep synergy of theoretical insights. We first establish the convergence condition for ensuring the convergence of the solution trajectory of ISHD. Then, we show that provided the stability condition, another relaxed requirement on the coefficients of ISHD, the sequence generated through the explicit Euler discretization of ISHD converges, which gives a large family of practical optimization methods. In order to select the best optimization method in this family for certain problems, we introduce the stopping time, the time required for an optimization method derived from ISHD to achieve a predefined level of suboptimality. Then, we formulate a novel learning to optimize (L2O) problem aimed at minimizing the stopping time subject to the convergence and stability condition. To navigate this learning problem, we present an algorithm combining stochastic optimization and the penalty method (StoPM). The convergence of StoPM using the conservative gradient is proved. Empirical validation of our framework is conducted through extensive numerical experiments across a diverse set of optimization problems. These experiments showcase the superior performance of the learned optimization methods.

Recent advances in robot skill learning have unlocked the potential to construct task-agnostic skill libraries, facilitating the seamless sequencing of multiple simple manipulation primitives (aka. skills) to tackle significantly more complex tasks. Nevertheless, determining the optimal sequence for independently learned skills remains an open problem, particularly when the objective is given solely in terms of the final geometric configuration rather than a symbolic goal. To address this challenge, we propose Logic-Skill Programming (LSP), an optimization-based approach that sequences independently learned skills to solve long-horizon tasks. We formulate a first-order extension of a mathematical program to optimize the overall cumulative reward of all skills within a plan, abstracted by the sum of value functions. To solve such programs, we leverage the use of tensor train factorization to construct the value function space, and rely on alternations between symbolic search and skill value optimization to find the appropriate skill skeleton and optimal subgoal sequence. Experimental results indicate that the obtained value functions provide a superior approximation of cumulative rewards compared to state-of-the-art reinforcement learning methods. Furthermore, we validate LSP in three manipulation domains, encompassing both prehensile and non-prehensile primitives. The results demonstrate its capability to identify the optimal solution over the full logic and geometric path. The real-robot experiments showcase the effectiveness of our approach to cope with contact uncertainty and external disturbances in the real world.

We propose a novel analysis framework for non-descent-type optimization methodologies in nonconvex scenarios based on the Kurdyka-Lojasiewicz property. Our framework allows covering a broad class of algorithms, including those commonly employed in stochastic and distributed optimization. Specifically, it enables the analysis of first-order methods that lack a sufficient descent property and do not require access to full (deterministic) gradient information. We leverage this framework to establish, for the first time, iterate convergence and the corresponding rates for the decentralized gradient method and federated averaging under mild assumptions. Furthermore, based on the new analysis techniques, we show the convergence of the random reshuffling and stochastic gradient descent method without necessitating typical a priori bounded iterates assumptions.

While Multi-view Graph Neural Networks (MVGNNs) excel at leveraging diverse modalities for learning object representation, existing methods assume identical local topology structures across modalities that overlook real-world discrepancies. This leads MVGNNs straggles in modality fusion and representations denoising. To address these issues, we propose adaptive modality-wise structure learning (AMoSL). To enable efficient end-to-end training, we employ an efficient solution for the resulting complex bilevel optimization problem. The effectiveness of AMoSL is demonstrated by its ability to train more accurate graph classifiers on six benchmark datasets. NTRODUCTION A large amount of data networks exhibits a unique structure known as graph-structured data. Irregular, non-Euclidean data characterize this data type and are frequently found in areas such as recommendation systems [1], social media networks [2], knowledge graphs [3], and molecular structures [4]. The analysis of graph-structured data has garnered substantial attention for its inherent inductive and transductive properties, which enable relational reasoning among entities (nodes) and their connections (edges). Graph Neural Networks (GNNs), through a series of advancements [5][6][7][8][9][10][11][12][13], have shown promising improvement in studying graph-structured data to conduct various downstream graph-related tasks.

Spiking neural networks (SNNs) have gained prominence for their potential in neuromorphic computing and energy-efficient artificial intelligence, yet optimizing them remains a formidable challenge for gradient-based methods due to their discrete, spike-based computation. This paper attempts to tackle the challenges by introducing Cosine Annealing Differential Evolution (CADE), designed to modulate the mutation factor (F) and crossover rate (CR) of differential evolution (DE) for the SNN model, i.e., Spiking Element Wise (SEW) ResNet. Extensive empirical evaluations were conducted to analyze CADE. CADE showed a balance in exploring and exploiting the search space, resulting in accelerated convergence and improved accuracy compared to existing gradient-based and DE-based methods. Moreover, an initialization method based on a transfer learning setting was developed, pretraining on a source dataset (i.e., CIFAR-10) and fine-tuning the target dataset (i.e., CIFAR-100), to improve population diversity. It was found to further enhance CADE for SNN. Remarkably, CADE elevates the performance of the highest accuracy SEW model by an additional 0.52 percentage points, underscoring its effectiveness in fine-tuning and enhancing SNNs. These findings emphasize the pivotal role of a scheduler for F and CR adjustment, especially for DE-based SNN. Source Code on Github: https://github.com/Tank-Jiang/CADE4SNN.

We consider the problem of optimizing initial conditions and timing in dynamical systems governed by unknown ordinary differential equations (ODEs), where evaluating different initial conditions is costly and there are constraints on observation times. To identify the optimal conditions within several trials, we introduce a few-shot Bayesian Optimization (BO) framework based on the system's prior information. At the core of our approach is the System-Aware Neural ODE Processes (SANODEP), an extension of Neural ODE Processes (NODEP) designed to meta-learn ODE systems from multiple trajectories using a novel context embedding block. Additionally, we propose a multi-scenario loss function specifically for optimization purposes. Our two-stage BO framework effectively incorporates search space constraints, enabling efficient optimization of both initial conditions and observation timings. We conduct extensive experiments showcasing SANODEP's potential for few-shot BO. We also explore SANODEP's adaptability to varying levels of prior information, highlighting the trade-off between prior flexibility and model fitting accuracy.

In contextual optimization, a decision-maker observes historical samples of uncertain variables and associated concurrent covariates, without knowing their joint distribution. Given an additional covariate observation, the goal is to choose a decision that minimizes some operational costs. A prevalent issue here is covariate shift, where the marginal distribution of the new covariate differs from historical samples, leading to decision performance variations with nonparametric or parametric estimators. To address this, we propose a distributionally robust approach that uses an ambiguity set by the intersection of two Wasserstein balls, each centered on typical nonparametric or parametric distribution estimators. Computationally, we establish the tractable reformulation of this distributionally robust optimization problem. Statistically, we provide guarantees for our Wasserstein ball intersection approach under covariate shift by analyzing the measure concentration of the estimators. Furthermore, to reduce computational complexity, we employ a surrogate objective that maintains similar generalization guarantees. Through synthetic and empirical case studies on income prediction and portfolio optimization, we demonstrate the strong empirical performance of our proposed models.