Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective (Betancourt et al., 2018). This has opened up the possibility of introducing variational and symplectic methods using geometric integration. In particular, in this paper, we introduce variational integrators (Marsden and West, 2001) which allow us to derive different methods for optimization. Using both, Hamilton's and Lagrange-d'Alembert's principle, we derive two families of optimization methods in one-to-one correspondence that generalize Polyak's heavy ball (Polyak, 1964) and Nesterov's accelerated gradient (Nesterov, 1983), the second of which mimics the behavior of the latter reducing the oscillations of classical momentum methods. However, since the systems considered are explicitly time-dependent, the preservation of symplecticity of autonomous systems occurs here solely on the fibers.

The Federated Learning (FL) paradigm is known to face challenges under heterogeneous client data. Local training on non-iid distributed data results in deflected local optimum, which causes the client models drift further away from each other and degrades the aggregated global model's performance. A natural solution is to gather all client data onto the server, such that the server has a global view of the entire data distribution. Unfortunately, this reduces to regular training, which compromises clients' privacy and conflicts with the purpose of FL. In this paper, we put forth an idea to collect and leverage global knowledge on the server without hindering data privacy. We unearth such knowledge from the dynamics of the global model's trajectory. Specifically, we first reserve a short trajectory of global model snapshots on the server. Then, we synthesize a small pseudo dataset such that the model trained on it mimics the dynamics of the reserved global model trajectory. Afterward, the synthesized data is used to help aggregate the deflected clients into the global model. We name our method Dynafed, which enjoys the following advantages: 1) we do not rely on any external on-server dataset, which requires no additional cost for data collection; 2) the pseudo data can be synthesized in early communication rounds, which enables Dynafed to take effect early for boosting the convergence and stabilizing training; 3) the pseudo data only needs to be synthesized once and can be directly utilized on the server to help aggregation in subsequent rounds. Experiments across extensive benchmarks are conducted to showcase the effectiveness of Dynafed. We also provide insights and understanding of the underlying mechanism of our method.

We show that Contrastive Learning (CL) under a broad family of loss functions (including InfoNCE) has a unified formulation of coordinate-wise optimization on the network parameter $\boldsymbol{\theta}$ and pairwise importance $\alpha$, where the \emph{max player} $\boldsymbol{\theta}$ learns representation for contrastiveness, and the \emph{min player} $\alpha$ puts more weights on pairs of distinct samples that share similar representations. The resulting formulation, called $\alpha$-CL, unifies not only various existing contrastive losses, which differ by how sample-pair importance $\alpha$ is constructed, but also is able to extrapolate to give novel contrastive losses beyond popular ones, opening a new avenue of contrastive loss design. These novel losses yield comparable (or better) performance on CIFAR10, STL-10 and CIFAR-100 than classic InfoNCE. Furthermore, we also analyze the max player in detail: we prove that with fixed $\alpha$, max player is equivalent to Principal Component Analysis (PCA) for deep linear network, and almost all local minima are global and rank-1, recovering optimal PCA solutions. Finally, we extend our analysis on max player to 2-layer ReLU networks, showing that its fixed points can have higher ranks.

In this paper, we consider a large-scale instance of the classical Pickup-and-Delivery Vehicle Routing Problem (PDVRP) that must be solved by a network of mobile cooperating robots. Robots must self-coordinate and self-allocate a set of pickup/delivery tasks while minimizing a given cost figure. This results in a large, challenging Mixed-Integer Linear Problem that must be cooperatively solved % without a central coordinator. We propose a distributed algorithm based on a primal decomposition approach that provides a feasible solution to the problem in finite time. An interesting feature of the proposed scheme is that each robot computes only its own block of solution, thereby preserving privacy of sensible information. The algorithm also exhibits attractive scalability properties that guarantee solvability of the problem even in large networks. To the best of our knowledge, this is the first attempt to provide a scalable distributed solution to the problem. The algorithm is first tested through Gazebo simulations on a ROS~2 platform, highlighting the effectiveness of the proposed solution. Finally, experiments on a real testbed with a team of ground and aerial robots are provided.

The unaffordable computation load of nonlinear model predictive control (NMPC) has prevented it for being used in robots with high sampling rates for decades. This paper is concerned with the policy learning problem for nonlinear MPC with system constraints, and its applications to unmanned surface vehicles (USVs), where the nonlinear MPC policy is learned offline and deployed online to resolve the computational complexity issue. A deep neural networks (DNN) based policy learning MPC (PL-MPC) method is proposed to avoid solving nonlinear optimal control problems online. The detailed policy learning method is developed and the PL-MPC algorithm is designed. The strategy to ensure the practical feasibility of policy implementation is proposed, and it is theoretically proved that the closed-loop system under the proposed method is asymptotically stable in probability. In addition, we apply the PL-MPC algorithm successfully to the motion control of USVs. It is shown that the proposed algorithm can be implemented at a sampling rate up to $5 Hz$ with high-precision motion control. The experiment video is available via:\url{https://v.youku.com/v_show/id_XNTkwMTM0NzM5Ng==.html

Integer programming problems (IPs) are challenging to be solved efficiently due to the NP-hardness, especially for large-scale IPs. To solve this type of IPs, Large neighborhood search (LNS) uses an initial feasible solution and iteratively improves it by searching a large neighborhood around the current solution. However, LNS easily steps into local optima and ignores the correlation between variables to be optimized, leading to compromised performance. This paper presents a general adaptive constraint partition-based optimization framework (ACP) for large-scale IPs that can efficiently use any existing optimization solver as a subroutine. Specifically, ACP first randomly partitions the constraints into blocks, where the number of blocks is adaptively adjusted to avoid local optima. Then, ACP uses a subroutine solver to optimize the decision variables in a randomly selected block of constraints to enhance the variable correlation. ACP is compared with LNS framework with different subroutine solvers on four IPs and a real-world IP. The experimental results demonstrate that in specified wall-clock time ACP shows better performance than SCIP and Gurobi.

This paper analyzes how the presence of service stations on highways affects traffic congestion. We focus on the problem of optimally designing a service station to achieve beneficial effects in terms of total traffic congestion and peak traffic reduction. Microsimulators cannot be used for this task due to their computational inefficiency. We propose a genetic algorithm based on the recently proposed CTMs, that efficiently describes the dynamics of a service station. Then, we leverage the algorithm to train a neural network capable of solving the same problem, avoiding implementing the CTMs. Finally, we examine two case studies to validate the capabilities and performance of our algorithms. In these simulations, we use real data extracted from Dutch highways.

Extensive efforts have been made to understand and improve the fairness of machine learning models based on observational metrics, especially in high-stakes domains such as medical insurance, education, and hiring decisions. However, there is a lack of certified fairness considering the end-to-end performance of an ML model. In this paper, we first formulate the certified fairness of an ML model trained on a given data distribution as an optimization problem based on the model performance loss bound on a fairness constrained distribution, which is within bounded distributional distance with the training distribution. We then propose a general fairness certification framework and instantiate it for both sensitive shifting and general shifting scenarios. In particular, we propose to solve the optimization problem by decomposing the original data distribution into analytical subpopulations and proving the convexity of the subproblems to solve them. We evaluate our certified fairness on six real-world datasets and show that our certification is tight in the sensitive shifting scenario and provides non-trivial certification under general shifting. Our framework is flexible to integrate additional non-skewness constraints and we show that it provides even tighter certification under different real-world scenarios. We also compare our certified fairness bound with adapted existing distributional robustness bounds on Gaussian data and demonstrate that our method is significantly tighter.

State-of-the-art reinforcement learning (RL) algorithms typically use random sampling (e.g., $\epsilon$-greedy) for exploration, but this method fails on hard exploration tasks like Montezuma's Revenge. To address the challenge of exploration, prior works incentivize exploration by rewarding the agent when it visits novel states. Such intrinsic rewards (also called exploration bonus or curiosity) often lead to excellent performance on hard exploration tasks. However, on easy exploration tasks, the agent gets distracted by intrinsic rewards and performs unnecessary exploration even when sufficient task (also called extrinsic) reward is available. Consequently, such an overly curious agent performs worse than an agent trained with only task reward. Such inconsistency in performance across tasks prevents the widespread use of intrinsic rewards with RL algorithms. We propose a principled constrained optimization procedure called Extrinsic-Intrinsic Policy Optimization (EIPO) that automatically tunes the importance of the intrinsic reward: it suppresses the intrinsic reward when exploration is unnecessary and increases it when exploration is required. The results is superior exploration that does not require manual tuning in balancing the intrinsic reward against the task reward. Consistent performance gains across sixty-one ATARI games validate our claim. The code is available at https://github.com/Improbable-AI/eipo.

Through ML we can address SE problems that cannot be completely algorithmically modeled, or for which existing solutions do not provide satisfactory results yet (e.g., defect/fault detection [16, 165, 180]). In addition, ML finds application in SE tasks where data cannot be easily analyzed with other algorithms (e.g., software requirements, code comments, code reviews, issues [9, 91, 174]). Another important aspect of ML is that it can significantly reduce manual effort in common SE tasks (e.g., automatic program repair [157], code suggestion [61], defect prediction [19], malware detection [147], feature location [40]) with great accuracy results [146, 164]. In fields such as health informatics ML and SE are considered complementary disciplines, since the growing scale and complexity of healthcare datasets have posed a challenge for clinical practice and medical research, requiring new engineering approaches from both fields [38]. In the early nineties, Huff and Selfridge [68] recognized the need for creating software systems that partially take some responsibility for their own evolution, offering the ability to implement, measure, and assess changes easily. These changes should also contribute to the overall improvement of the corresponding systems [142].