Federated Learning (FL) is a distributed machine learning (ML) paradigm, in which multiple clients collaboratively train ML models without centralizing their local data. Similar to conventional ML pipelines, the client local optimization and server aggregation procedure in FL are sensitive to the hyperparameter (HP) selection. Despite extensive research on tuning HPs for centralized ML, these methods yield suboptimal results when employed in FL. This is mainly because their "training-after-tuning" framework is unsuitable for FL with limited client computation power. While some approaches have been proposed for HP-Tuning in FL, they are limited to the HPs for client local updates. In this work, we propose a novel HP-tuning algorithm, called Federated Population-based Hyperparameter Tuning (FedPop), to address this vital yet challenging problem. FedPop employs population-based evolutionary algorithms to optimize the HPs, which accommodates various HP types at both client and server sides. Compared with prior tuning methods, FedPop employs an online "tuning-while-training" framework, offering computational efficiency and enabling the exploration of a broader HP search space. Our empirical validation on the common FL benchmarks and complex real-world FL datasets demonstrates the effectiveness of the proposed method, which substantially outperforms the concurrent state-of-the-art HP tuning methods for FL.

Large language models (LLMs), such as ChatGPT and GPT4, have shown outstanding performance in many human life task. Attention computation plays an important role in training LLMs. Softmax unit and ReLU unit are the key structure in attention computation. Inspired by them, we put forward a softmax ReLU regression problem. Generally speaking, our goal is to find an optimal solution to the regression problem involving the ReLU unit. In this work, we calculate a close form representation for the Hessian of the loss function. Under certain assumptions, we prove the Lipschitz continuous and the PSDness of the Hessian. Then, we introduce an greedy algorithm based on approximate Newton method, which converges in the sense of the distance to optimal solution. Last, We relax the Lipschitz condition and prove the convergence in the sense of loss value.

We consider the fundamental task of optimizing a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in statistical inference. We use the warped Riemannian geometry notions to redefine the optimisation problem of a function on Euclidean space to a Riemannian manifold with a warped metric, and then find the function's optimum along this manifold. The warped metric chosen for the search domain induces a computational friendly metric-tensor for which optimal search directions associate with geodesic curves on the manifold becomes easier to compute. Performing optimization along geodesics is known to be generally infeasible, yet we show that in this specific manifold we can analytically derive Taylor approximations up to third-order. In general these approximations to the geodesic curve will not lie on the manifold, however we construct suitable retraction maps to pull them back onto the manifold. Therefore, we can efficiently optimize along the approximate geodesic curves. We cover the related theory, describe a practical optimization algorithm and empirically evaluate it on a collection of challenging optimisation benchmarks. Our proposed algorithm, using third-order approximation of geodesics, outperforms standard Euclidean gradient-based counterparts in term of number of iterations until convergence and an alternative method for Hessian-based optimisation routines.

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning. To overcome this challenge, robust satisficing (RS) seeks a robust solution to an unspecified distributional shift while achieving a utility above a desired threshold. This paper focuses on the problem of RS in contextual Bayesian optimization when there is a discrepancy between the true and reference distributions of the context. We propose a novel robust Bayesian satisficing algorithm called RoBOS for noisy black-box optimization. Our algorithm guarantees sublinear lenient regret under certain assumptions on the amount of distribution shift. In addition, we define a weaker notion of regret called robust satisficing regret, in which our algorithm achieves a sublinear upper bound independent of the amount of distribution shift. To demonstrate the effectiveness of our method, we apply it to various learning problems and compare it to other approaches, such as distributionally robust optimization.

Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze stochastic algorithms that apply to both non-convex and convex losses for solving Kullback Leibler divergence constrained DRO problem. Compared with existing methods solving this problem, our stochastic algorithms not only enjoy competitive if not better complexity independent of sample size but also just require a constant batch size at every iteration, which is more practical for broad applications. We establish a nearly optimal complexity bound for finding an $\epsilon$ stationary solution for non-convex losses and an optimal complexity for finding an $\epsilon$ optimal solution for convex losses. Empirical studies demonstrate the effectiveness of the proposed algorithms for solving non-convex and convex constrained DRO problems.

We propose fast and communication-efficient optimization algorithms for multi-robot rotation averaging and translation estimation problems that arise from collaborative simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and camera network localization applications. Our methods are based on theoretical relations between the Hessians of the underlying Riemannian optimization problems and the Laplacians of suitably weighted graphs. We leverage these results to design a collaborative solver in which robots coordinate with a central server to perform approximate second-order optimization, by solving a Laplacian system at each iteration. Crucially, our algorithms permit robots to employ spectral sparsification to sparsify intermediate dense matrices before communication, and hence provide a mechanism to trade off accuracy with communication efficiency with provable guarantees. We perform rigorous theoretical analysis of our methods and prove that they enjoy (local) linear rate of convergence. Furthermore, we show that our methods can be combined with graduated non-convexity to achieve outlier-robust estimation. Extensive experiments on real-world SLAM and SfM scenarios demonstrate the superior convergence rate and communication efficiency of our methods.

This paper presents a study on the use of the Talos humanoid robot for performing assistive sit-to-stand or stand-to-sit tasks. In such tasks, the human exerts a large amount of force (100--200 N) within a very short time (2--8 s), posing significant challenges in terms of human unpredictability and robot stability control. To address these challenges, we propose an approach for finding a spatial reference for the robot, which allows the robot to move according to the force exerted by the human and control its stability during the task. Specifically, we focus on the problem of finding a 1D manifold for the robot, while assuming a simple controller to guide its movement on this manifold. To achieve this, we use a functional representation to parameterize the manifold and solve an optimization problem that takes into account the robot's stability and the unpredictability of human behavior. We demonstrate the effectiveness of our approach through simulations and experiments with the Talos robot, showing robustness and adaptability.

The performance of robots in high-level tasks depends on the quality of their lower-level controller, which requires fine-tuning. However, the intrinsically nonlinear dynamics and controllers make tuning a challenging task when it is done by hand. In this paper, we present DiffTune, a novel, gradient-based automatic tuning framework. We formulate the controller tuning as a parameter optimization problem. Our method unrolls the dynamical system and controller as a computational graph and updates the controller parameters through gradient-based optimization. The gradient is obtained using sensitivity propagation, which is the only method for gradient computation when tuning for a physical system instead of its simulated counterpart. Furthermore, we use $\mathcal{L}_1$ adaptive control to compensate for the uncertainties (that unavoidably exist in a physical system) such that the gradient is not biased by the unmodelled uncertainties. We validate the DiffTune on a Dubin's car and a quadrotor in challenging simulation environments. In comparison with state-of-the-art auto-tuning methods, DiffTune achieves the best performance in a more efficient manner owing to its effective usage of the first-order information of the system. Experiments on tuning a nonlinear controller for quadrotor show promising results, where DiffTune achieves 3.5x tracking error reduction on an aggressive trajectory in only 10 trials over a 12-dimensional controller parameter space.

High-level synthesis (HLS) is a process that automatically translates a software program in a high-level language into a low-level hardware description. However, the hardware designs produced by HLS tools still suffer from a significant performance gap compared to manual implementations. This is because the input HLS programs must still be written using hardware design principles. Existing techniques either leave the program source unchanged or perform a fixed sequence of source transformation passes, potentially missing opportunities to find the optimal design. We propose a super-optimization approach for HLS that automatically rewrites an arbitrary software program into efficient HLS code that can be used to generate an optimized hardware design. We developed a toolflow named SEER, based on the e-graph data structure, to efficiently explore equivalent implementations of a program at scale. SEER provides an extensible framework, orchestrating existing software compiler passes and hardware synthesis optimizers. Our work is the first attempt to exploit e-graph rewriting for large software compiler frameworks, such as MLIR. Across a set of open-source benchmarks, we show that SEER achieves up to 38x the performance within 1.4x the area of the original program. Via an Intel-provided case study, SEER demonstrates the potential to outperform manually optimized designs produced by hardware experts.

Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP), which can be solved by general-purpose off-the-shelf MICP solvers. To mitigate the scalability challenge of solving these MICP problems, existing work focuses on devising efficient and strong formulations of the problems, while less effort has been spent on exploiting their specific structure to develop specialized solvers. The latter is the theme of our work. We focus on efficiently handling one-hot constraints, which are particularly relevant when encoding PWA dynamics. We have implemented our techniques in a tool, Soy, which organically integrates logical reasoning, arithmetic reasoning, and stochastic local search. For a set of PWA control benchmarks, Soy solves more problems, faster, than two state-of-the-art MICP solvers.