A Low-rank Spectral Optimization Problem (LSOP) minimizes a linear objective subject to multiple two-sided linear matrix inequalities intersected with a low-rank and spectral constrained domain set. Although solving LSOP is, in general, NP-hard, its partial convexification (i.e., replacing the domain set by its convex hull) termed "LSOP-R," is often tractable and yields a high-quality solution. This motivates us to study the strength of LSOP-R. Specifically, we derive rank bounds for any extreme point of the feasible set of LSOP-R and prove their tightness for the domain sets with different matrix spaces. The proposed rank bounds recover two well-known results in the literature from a fresh angle and also allow us to derive sufficient conditions under which the relaxation LSOP-R is equivalent to the original LSOP. To effectively solve LSOP-R, we develop a column generation algorithm with a vector-based convex pricing oracle, coupled with a rank-reduction algorithm, which ensures the output solution satisfies the theoretical rank bound. Finally, we numerically verify the strength of the LSOP-R and the efficacy of the proposed algorithms.

The interplay between learning and evolution has been studied for decades, but it is still a very controversial topic. Despite the huge amount of work, to what extent the interaction between learning and evolution actually fosters the development of successful behaviors is still a matter of debate in the scientific community. Indeed, as it is well described in [1-2], there exist some controversial arguments about the effect of learning on evolution. Some studies revealed how learning accelerates evolution [3-15], while other works demonstrated that learning does not provide any advantage on the course of evolution [16-24]. As explained in [25], Evolution and learning (or phylogenetic and ontogenetic adaptation) are two forms of biological adaptation that differ in space and time. Evolution is a process of selective reproduction and substitution based on the existence of a population of individuals displaying variability at the genetic level.

We study the problem of computing an optimal policy of an infinite-horizon discounted constrained Markov decision process (constrained MDP). Despite the popularity of Lagrangian-based policy search methods used in practice, the oscillation of policy iterates in these methods has not been fully understood, bringing out issues such as violation of constraints and sensitivity to hyper-parameters. To fill this gap, we employ the Lagrangian method to cast a constrained MDP into a constrained saddle-point problem in which max/min players correspond to primal/dual variables, respectively, and develop two single-time-scale policy-based primal-dual algorithms with non-asymptotic convergence of their policy iterates to an optimal constrained policy. Specifically, we first propose a regularized policy gradient primal-dual (RPG-PD) method that updates the policy using an entropy-regularized policy gradient, and the dual via a quadratic-regularized gradient ascent, simultaneously. We prove that the policy primal-dual iterates of RPG-PD converge to a regularized saddle point with a sublinear rate, while the policy iterates converge sublinearly to an optimal constrained policy. We further instantiate RPG-PD in large state or action spaces by including function approximation in policy parametrization, and establish similar sublinear last-iterate policy convergence. Second, we propose an optimistic policy gradient primal-dual (OPG-PD) method that employs the optimistic gradient method to update primal/dual variables, simultaneously. We prove that the policy primal-dual iterates of OPG-PD converge to a saddle point that contains an optimal constrained policy, with a linear rate. To the best of our knowledge, this work appears to be the first non-asymptotic policy last-iterate convergence result for single-time-scale algorithms in constrained MDPs.

Network slicing enables operators to efficiently support diverse applications on a common physical infrastructure. The ever-increasing densification of network deployment leads to complex and non-trivial inter-cell interference, which requires more than inaccurate analytic models to dynamically optimize resource management for network slices. In this paper, we develop a DIRP algorithm with multiple deep reinforcement learning (DRL) agents to cooperatively optimize resource partition in individual cells to fulfill the requirements of each slice, based on two alternative reward functions. Nevertheless, existing DRL approaches usually tie the pretrained model parameters to specific network environments with poor transferability, which raises practical deployment concerns in large-scale mobile networks. Hence, we design a novel transfer learning-aided DIRP (TL-DIRP) algorithm to ease the transfer of DIRP agents across different network environments in terms of sample efficiency, model reproducibility, and algorithm scalability. The TL-DIRP algorithm first centrally trains a generalized model and then transfers the "generalist" to each local agent as "specialist" with distributed finetuning and execution. TL-DIRP consists of two steps: 1) centralized training of a generalized distributed model, 2) transferring the "generalist" to each "specialist" with distributed finetuning and execution. The numerical results show that not only DIRP outperforms existing baseline approaches in terms of faster convergence and higher reward, but more importantly, TL-DIRP significantly improves the service performance, with reduced exploration cost, accelerated convergence rate, and enhanced model reproducibility. As compared to a traffic-aware baseline, TL-DIRP provides about 15% less violation ratio of the quality of service (QoS) for the worst slice service and 8.8% less violation on the average service QoS.

Robots are increasingly being deployed not only in workplaces but also in households. Effectively execute of manipulation tasks by robots relies on variable impedance control with contact forces. Furthermore, robots should possess adaptive capabilities to handle the considerable variations exhibited by different robotic tasks in dynamic environments, which can be obtained through human demonstrations. This paper presents a learning-from-demonstration framework that integrates force sensing and motion information to facilitate variable impedance control. The proposed approach involves the estimation of full stiffness matrices from human demonstrations, which are then combined with sensed forces and motion information to create a model using the non-parametric method. This model allows the robot to replicate the demonstrated task while also responding appropriately to new task conditions through the use of the state-dependent stiffness profile. Additionally, a novel tank based variable impedance control approach is proposed to ensure passivity by using the learned stiffness. The proposed approach was evaluated using two virtual variable stiffness systems. The first evaluation demonstrates that the stiffness estimated approach exhibits superior robustness compared to traditional methods when tested on manual datasets, and the second evaluation illustrates that the novel tank based approach is more easily implementable compared to traditional variable impedance control approaches.

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and has significant impacts in industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary solutions. Motivated by the new characterizations, we develop an efficient local search solver, which is the first local search solver for general ILP validated on a large heterogeneous problem dataset. We propose a new local search framework that switches between three modes, namely Search, Improve, and Restore modes. We design tailored operators adapted to different modes, thus improving the quality of the current solution according to different situations. For the Search and Restore modes, we propose an operator named tight move, which adaptively modifies variables' values, trying to make some constraint tight. For the Improve mode, an efficient operator lift move is proposed to improve the quality of the objective function while maintaining feasibility. Putting these together, we develop a local search solver for integer linear programming called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our solver in solving large-scale hard integer linear programming problems within a reasonably short time. Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our solver establishes new records for 6 MIPLIB open instances. The theoretical analysis of our algorithm is also presented, which shows our algorithm could avoid visiting unnecessary regions and also maintain good connectivity of targeted solutions.

Machine learning (ML) methods are used in most technical areas such as image recognition, product recommendation, financial analysis, medical diagnosis, and predictive maintenance. An important aspect of implementing ML methods involves controlling the learning process for the ML method so as to maximize the performance of the method under consideration. Hyperparameter tuning is the process of selecting a suitable set of ML method parameters that control its learning process. In this work, we demonstrate the use of discrete simulation optimization methods such as ranking and selection (R&S) and random search for identifying a hyperparameter set that maximizes the performance of a ML method. Specifically, we use the KN R&S method and the stochastic ruler random search method and one of its variations for this purpose. We also construct the theoretical basis for applying the KN method, which determines the optimal solution with a statistical guarantee via solution space enumeration. In comparison, the stochastic ruler method asymptotically converges to global optima and incurs smaller computational overheads. We demonstrate the application of these methods to a wide variety of machine learning models, including deep neural network models used for time series prediction and image classification. We benchmark our application of these methods with state-of-the-art hyperparameter optimization libraries such as $hyperopt$ and $mango$. The KN method consistently outperforms $hyperopt$'s random search (RS) and Tree of Parzen Estimators (TPE) methods. The stochastic ruler method outperforms the $hyperopt$ RS method and offers statistically comparable performance with respect to $hyperopt$'s TPE method and the $mango$ algorithm.

Optimal control of general nonlinear systems is a central challenge in automation. Enabled by powerful function approximators, data-driven approaches to control have recently successfully tackled challenging applications. However, such methods often obscure the structure of dynamics and control behind black-box over-parameterized representations, thus limiting our ability to understand closed-loop behavior. This paper adopts a hybrid-system view of nonlinear modeling and control that lends an explicit hierarchical structure to the problem and breaks down complex dynamics into simpler localized units. We consider a sequence modeling paradigm that captures the temporal structure of the data and derive an expectation-maximization (EM) algorithm that automatically decomposes nonlinear dynamics into stochastic piecewise affine models with nonlinear transition boundaries. Furthermore, we show that these time-series models naturally admit a closed-loop extension that we use to extract local polynomial feedback controllers from nonlinear experts via behavioral cloning. Finally, we introduce a novel hybrid relative entropy policy search (Hb-REPS) technique that incorporates the hierarchical nature of hybrid models and optimizes a set of time-invariant piecewise feedback controllers derived from a piecewise polynomial approximation of a global state-value function.

Achieving the economical and stable operation of Multi-microgrids (MMG) systems is vital. However, there are still some challenging problems to be solved. Firstly, from the perspective of stable operation, it is necessary to minimize the energy fluctuation of the main grid. Secondly, the characteristics of energy conversion equipment need to be considered. Finally, privacy protection while reducing the operating cost of an MMG system is crucial. To address these challenges, a Data-driven strategy for MMG systems with Shared Energy Storage (SES) is proposed. The Mixed-Attention is applied to fit the conditions of the equipment, additionally, Multi-Agent Soft Actor-Critic(MA-SAC) and (Multi-Agent Win or Learn Fast Policy Hill-Climbing)MA-WoLF-PHC are proposed to solve the partially observable dynamic stochastic game problem. By testing the operation data of the MMG system in Northwest China, following conclusions are drawn: the R-Square (R2) values of results reach 0.999, indicating the neural network effectively models the nonlinear conditions. The proposed MMG system framework can reduce energy fluctuations in the main grid by 1746.5kW in 24 hours and achieve a cost reduction of 16.21% in the test. Finally, the superiority of the proposed algorithms is verified through their fast convergence speed and excellent optimization performance.