State-of-the-art methods for solving 2-player zero-sum imperfect information games rely on linear programming or regret minimization, though not on dynamic programming (DP) or heuristic search (HS), while the latter are often at the core of state-of-the-art solvers for other sequential decision-making problems. In partially observable or collaborative settings (e.g., POMDPs and Dec- POMDPs), DP and HS require introducing an appropriate statistic that induces a fully observable problem as well as bounding (convex) approximators of the optimal value function. This approach has succeeded in some subclasses of 2-player zero-sum partially observable stochastic games (zs- POSGs) as well, but how to apply it in the general case still remains an open question. We answer it by (i) rigorously defining an equivalent game to work with, (ii) proving mathematical properties of the optimal value function that allow deriving bounds that come with solution strategies, (iii) proposing for the first time an HSVI-like solver that provably converges to an $\epsilon$-optimal solution in finite time, and (iv) empirically analyzing it. This opens the door to a novel family of promising approaches complementing those relying on linear programming or iterative methods.

Federated learning (FL) enables collaborative model training without centralizing data. However, the traditional FL framework is cloud-based and suffers from high communication latency. On the other hand, the edge-based FL framework that relies on an edge server co-located with mobile base station for model aggregation has low communication latency but suffers from degraded model accuracy due to the limited coverage of edge server. In light of high accuracy but high-latency cloud-based FL and low-latency but low-accuracy edge-based FL, this paper proposes a new FL framework based on cooperative mobile edge networking called cooperative federated edge learning (CFEL) to enable both high-accuracy and low-latency distributed intelligence at mobile edge networks. Considering the unique two-tier network architecture of CFEL, a novel federated optimization method dubbed cooperative edge-based federated averaging (CE-FedAvg) is further developed, wherein each edge server both coordinates collaborative model training among the devices within its own coverage and cooperates with other edge servers to learn a shared global model through decentralized consensus. Experimental results based on benchmark datasets show that CFEL can largely reduce the training time to achieve a target model accuracy compared with prior FL frameworks.

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the iterative optimization process. To accelerate such a procedure, we apply a numerical pipeline that involves artificial neural networks to parametrize the boundary conditions of the problem in hand, compress the dimensionality of the (full-order) snapshots, and approximate the parametric solution manifold. It derives a general framework capable to provide an ad-hoc parametrization of the inlet boundary and quickly converges to the optimal solution thanks to model order reduction. We present in this contribution the results obtained by applying such methods to two different CFD test cases.

Abstract: In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that the value function is deterministic, and obtain the dynamic programming principle. Furthermore, we prove that the value function is the unique viscosity solution to the related HJB equation under degenerate case. Abstract: We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term.

Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite element analysis iterations required to evaluate the component's performance during the optimization process. Recently, machine learning (ML)-based topology optimization methods have been explored by researchers to alleviate this issue. However, previous ML approaches have mainly been demonstrated on simple two-dimensional applications with low-resolution geometry. Further, current methods are based on a single ML model for end-to-end prediction, which requires a large dataset for training. These challenges make it non-trivial to extend current approaches to higher resolutions. In this paper, we develop deep learning-based frameworks consistent with traditional topology optimization algorithms for 3D topology optimization with a reasonably fine (high) resolution. We achieve this by training multiple networks, each learning a different step of the overall topology optimization methodology, making the framework more consistent with the topology optimization algorithm. We demonstrate the application of our framework on both 2D and 3D geometries. The results show that our approach predicts the final optimized design better (5.76x reduction in total compliance MSE in 2D; 2.03x reduction in total compliance MSE in 3D) than current ML-based topology optimization methods.

We propose a method for maximum likelihood estimation of path choice model parameters and arc travel time using data of different levels of granularity. Hitherto these two tasks have been tackled separately under strong assumptions. Using a small example, we illustrate that this can lead to biased results. Results on both real (New York yellow cab) and simulated data show strong performance of our method compared to existing baselines.

Contact-rich manipulation is challenging due to dynamically-changing physical constraints by the contact mode changes undergone during manipulation. This paper proposes a versatile local planning and control framework for contact-rich manipulation that determines the continuous control action under variable contact modes online. We model the physical characteristics of contact-rich manipulation by quasistatic dynamics and complementarity constraints. We then propose a linear complementarity quadratic program (LCQP) to efficiently determine the control action that implicitly includes the decisions on the contact modes under these constraints. In the LCQP, we relax the complementarity constraints to alleviate ill-conditioned problems that are typically caused by measure noises or model miss-matches. We conduct dynamical simulations on a 3D physical simulator and demonstrate that the proposed method can achieve various contact-rich manipulation tasks by determining the control action including the contact modes in real-time.

The requirements of modern production systems together with more advanced robotic technologies have fostered the integration of teams comprising humans and autonomous robots. However, along with the potential benefits also comes the question of how to effectively handle these teams considering the different characteristics of the involved agents. For this reason, this paper presents a framework for task allocation in a human multi-robot collaborative scenario. The proposed solution combines an optimal offline allocation with an online reallocation strategy which accounts for inaccuracies of the offline plan and/or unforeseen events, human subjective preferences and cost of switching from one task to another so as to increase human satisfaction and team efficiency. Experiments are presented for the case of two manipulators cooperating with a human operator for performing a box filling task.

We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian gradient descent (RGD) and Riemannian Gauss-Newton (RGN) methods and cope with the challenge of unknown rank by studying the effect of rank over-parameterization. We provide the first convergence guarantee for the general tensor-on-tensor regression by showing that RGD and RGN respectively converge linearly and quadratically to a statistically optimal estimate in both rank correctly-parameterized and over-parameterized settings. Our theory reveals an intriguing phenomenon: Riemannian optimization methods naturally adapt to over-parameterization without modifications to their implementation. We also prove the statistical-computational gap in scalar-on-tensor regression by a direct low-degree polynomial argument. Our theory demonstrates a "blessing of statistical-computational gap" phenomenon: in a wide range of scenarios in tensor-on-tensor regression for tensors of order three or higher, the computationally required sample size matches what is needed by moderate rank over-parameterization when considering computationally feasible estimators, while there are no such benefits in the matrix settings. This shows moderate rank over-parameterization is essentially "cost-free" in terms of sample size in tensor-on-tensor regression of order three or higher. Finally, we conduct simulation studies to show the advantages of our proposed methods and to corroborate our theoretical findings.

Methods for combining Machine Learning (ML) and Constrained Optimization (CO) for decision support have attracted considerable interest in recent years. This is motivated by the possibility to tackle complex decision making problems subject to uncertainty (sometimes over multiple stages), and having a partially specified structure where knowledge is available both in explicit form (cost function, constraints) and implicit form (historical data or simulators). As a practical example, an Energy Management Systems (EMS) needs to allocate minimum-cost power flows from different Distributed Energy Resources (DERs) [1]. Based on actual energy prices, and forecasts on the availability of DERs and on consumption, the EMS decides which power generators should be used and whether the surplus should be stored or sold to the market. Such a problem involves hard constraints (maintaining power balance, power flow limits), a clear cost structure, elements of uncertainty that are partially known via historical data, and multiple decision stages likely subject to execution time restrictions. In this type of use case, pure CO methods struggle with robustness and scalability, while pure ML methods such as Reinforcement Learning (RL) have trouble dealing with hard constraints and combinatorial decision spaces. Motivated by the opportunity to obtain improvements via a combination of ML and CO, multiple lines of research have emerged, such as Decision Focused Learning, Constrained Reinforcement Learning, or Algorithm Configuration. While existing methods have obtained a good measure of success, to the best of the authors knowledge no existing method can deal with all the challenges we have identified. Ideally, one wishes to obtain a solution policy capable of providing feasible (and high-quality) solutions, handling robustness, taking advantage of existing data, and with a reasonable computational load.