The innovative Federated Multi-Task Learning (FMTL) approach consolidates the benefits of Federated Learning (FL) and Multi-Task Learning (MTL), enabling collaborative model training on multi-task learning datasets. However, a comprehensive evaluation method, integrating the unique features of both FL and MTL, is currently absent in the field. This paper fills this void by introducing a novel framework, FMTL-Bench, for systematic evaluation of the FMTL paradigm. This benchmark covers various aspects at the data, model, and optimization algorithm levels, and comprises seven sets of comparative experiments, encapsulating a wide array of non-independent and identically distributed (Non-IID) data partitioning scenarios. We propose a systematic process for comparing baselines of diverse indicators and conduct a case study on communication expenditure, time, and energy consumption. Through our exhaustive experiments, we aim to provide valuable insights into the strengths and limitations of existing baseline methods, contributing to the ongoing discourse on optimal FMTL application in practical scenarios. The source code can be found on https://github.com/youngfish42/FMTL-Benchmark .

The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative collision avoidance technique using the notion of convex optimization to establish the distance between robotic spacecraft and space structures for autonomous on-orbit assembly operations. The proposed technique defines each ellipsoidal- and polyhedral-shaped object as the union of convex compact sets, each represented non-conservatively by a real-valued convex function. Then, the functions are introduced as a set of constraints to a convex optimization problem to produce a new set of differentiable constraints resulting from the optimality conditions. These new constraints are later fed into an optimal control problem to enforce collision avoidance where the motion planning for the autonomous on-orbit assembly takes place. Numerical experiments for two assembly scenarios in tight environments are presented to demonstrate the capability and effectiveness of the proposed technique. The results show that this framework leads to optimal non-conservative trajectories for robotic spacecraft in tight environments. Although developed for autonomous on-orbit assembly, this technique could be used for any generic motion planning problem where collision avoidance is crucial.

Designing tests to evaluate if a given autonomous system satisfies complex specifications is challenging due to the complexity of these systems. This work proposes a flow-based approach for reactive test synthesis from temporal logic specifications, enabling the synthesis of test environments consisting of static and reactive obstacles and dynamic test agents. The temporal logic specifications describe desired test behavior, including system requirements as well as a test objective that is not revealed to the system. The synthesized test strategy places restrictions on system actions in reaction to the system state. The tests are minimally restrictive and accomplish the test objective while ensuring realizability of the system's objective without aiding it (semi-cooperative setting). Automata theory and flow networks are leveraged to formulate a mixed-integer linear program (MILP) to synthesize the test strategy. For a dynamic test agent, the agent strategy is synthesized for a GR(1) specification constructed from the solution of the MILP. If the specification is unrealizable by the dynamics of the test agent, a counterexample-guided approach is used to resolve the MILP until a strategy is found. This flow-based, reactive test synthesis is conducted offline and is agnostic to the system controller. Finally, the resulting test strategy is demonstrated in simulation and experimentally on a pair of quadrupedal robots for a variety of specifications.

One of the objectives of continual learning is to prevent catastrophic forgetting in learning multiple tasks sequentially, and the existing solutions have been driven by the conceptualization of the plasticity-stability dilemma. However, the convergence of continual learning for each sequential task is less studied so far. In this paper, we provide a convergence analysis of memory-based continual learning with stochastic gradient descent and empirical evidence that training current tasks causes the cumulative degradation of previous tasks. We propose an adaptive method for nonconvex continual learning (NCCL), which adjusts step sizes of both previous and current tasks with the gradients. The proposed method can achieve the same convergence rate as the SGD method when the catastrophic forgetting term which we define in the paper is suppressed at each iteration. Further, we demonstrate that the proposed algorithm improves the performance of continual learning over existing methods for several image classification tasks.

The need for fully autonomous mobile robots has surged over the past decade, with the imperative of ensuring safe navigation in a dynamic setting emerging as a primary challenge impeding advancements in this domain. In this paper, a Safety Critical Model Predictive Control based on Dynamic Feedback Linearization tailored to the application of differential drive robots with two wheels is proposed to generate control signals that result in obstacle-free paths. A barrier function introduces a safety constraint to the optimization problem of the Model Predictive Control (MPC) to prevent collisions. Due to the intrinsic nonlinearities of the differential drive robots, computational complexity while implementing a Nonlinear Model Predictive Control (NMPC) arises. To facilitate the real-time implementation of the optimization problem and to accommodate the underactuated nature of the robot, a combination of Linear Model Predictive Control (LMPC) and Dynamic Feedback Linearization (DFL) is proposed. The MPC problem is formulated on a linear equivalent model of the differential drive robot rendered by the DFL controller. The analysis of the closed-loop stability and recursive feasibility of the proposed control design is discussed. Numerical experiments illustrate the robustness and effectiveness of the proposed control synthesis in avoiding obstacles with respect to the benchmark of using Euclidean distance constraints. Keywords: Model Predictive Control, MPC, Autonomous Ground Vehicles, Nonlinearity, Dynamic Feedback Linearization, Optimal Control, Differential Robots.

Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well know examples of momentum-descent methods for optimization. While the latter outperforms the former, solely generalizations of PHB-like methods to nonlinear spaces have been described in the literature. We propose here a generalization of NAG-like methods for Lie group optimization based on the variational one-to-one correspondence between classical and accelerated momentum methods (Campos et al., 2023).

In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified framework for developing Lagrangian-based methods, which takes a single-step update to the primal variables by some subgradient methods in each iteration. These subgradient methods are ``embedded'' into our framework, in the sense that they are incorporated as black-box updates to the primal variables. We prove that our proposed framework inherits the global convergence guarantees from these embedded subgradient methods under mild conditions. In addition, we show that our framework can be extended to solve constrained optimization problems with expectation constraints. Based on the proposed framework, we show that a wide range of existing stochastic subgradient methods, including the proximal SGD, proximal momentum SGD, and proximal ADAM, can be embedded into Lagrangian-based methods. Preliminary numerical experiments on deep learning tasks illustrate that our proposed framework yields efficient variants of Lagrangian-based methods with convergence guarantees for nonconvex nonsmooth constrained optimization problems.

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation of distributions and thus could apply to distributions in different spaces. These properties make Gromov-Wasserstein widely applicable to many fields, such as computer graphics and machine learning. However, the computation of the Gromov-Wasserstein distance and transport plan is expensive. The well-known Entropic Gromov-Wasserstein approach has a cubic complexity since the matrix multiplication operations need to be repeated in computing the gradient of Gromov-Wasserstein loss. This becomes a key bottleneck of the method. Currently, existing methods accelerate the computation focus on sampling and approximation, which leads to low accuracy or incomplete transport plan. In this work, we propose a novel method to accelerate accurate gradient computation by dynamic programming techniques, reducing the complexity from cubic to quadratic. In this way, the original computational bottleneck is broken and the new entropic solution can be obtained with total quadratic time, which is almost optimal complexity. Furthermore, it can be extended to some variants easily. Extensive experiments validate the efficiency and effectiveness of our method.

Fairness in federated learning has emerged as a critical concern, aiming to develop an unbiased model for any special group (e.g., male or female) of sensitive features. However, there is a trade-off between model performance and fairness, i.e., improving fairness will decrease model performance. Existing approaches have characterized such a trade-off by introducing hyperparameters to quantify client's preferences for fairness and model performance. Nevertheless, these methods are limited to scenarios where each client has only a single pre-defined preference. In practical systems, each client may simultaneously have multiple preferences for the model performance and fairness. The key challenge is to design a method that allows the model to adapt to diverse preferences of each client in real time. To this end, we propose a Preference-aware scheme in Fair Federated Learning paradigm (called PraFFL). PraFFL can adaptively adjust the model based on each client's preferences to meet their needs. We theoretically prove that PraFFL can provide the optimal model for client's arbitrary preferences. Experimental results show that our proposed PraFFL outperforms five existing fair federated learning algorithms in terms of the model's capability in adapting to clients' different preferences.

This work proposes a novel method to generate C-Tests; a deviated form of cloze tests (a gap filling exercise) where only the last part of a word is turned into a gap. In contrast to previous works that only consider varying the gap size or gap placement to achieve locally optimal solutions, we propose a mixed-integer programming (MIP) approach. This allows us to consider gap size and placement simultaneously, achieving globally optimal solutions, and to directly integrate state-of-the-art models for gap difficulty prediction into the optimization problem. A user study with 40 participants across four C-Test generation strategies (including GPT-4) shows that our approach (MIP) significantly outperforms two of the baseline strategies (based on gap placement and GPT-4); and performs on-par with the third (based on gap size). Our analysis shows that GPT-4 still struggles to fulfill explicit constraints during generation and that MIP produces C-Tests that correlate best with the perceived difficulty. We publish our code, model, and collected data consisting of 32 English C-Tests with 20 gaps each (totaling 3,200 individual gap responses) under an open source license.