As demonstrated by Ratliff et al. (2014), inverse optimization can be used to recover the objective function parameters of players in multi-player Nash games. These games involve the optimization problems of multiple players in which the players can affect each other in their objective functions. In generalized Nash equilibrium problems (GNEPs), a player's set of feasible actions is also impacted by the actions taken by other players in the game; see Facchinei and Kanzow (2010) for more background on this problem. One example of such impact comes in the form of joint/"coupled" constraints as referenced by Rosen (1965), Harker (1991), and Facchinei et al. (2007) which involve other players' variables in the constraints of the feasible region. We extend the framework of Ratliff et al. (2014) to find inverse optimization solutions for the class of GNEPs with joint constraints. The resulting formulation is then applied to a simulated multi-player transportation problem on a road network. Also, we provide some theoretical results related to this transportation problem regarding runtime of the extended framework as well as uniqueness and non-uniqueness of solutions to our simulation experiments. We see that our model recovers parameterizations that produce the same flow patterns as the original parameterizations and that this holds true across multiple networks, different assumptions regarding players' perceived costs, and the majority of restrictive capacity settings and the associated numbers of players. Code for the project can be found at: https://github.com/sallen7/IO_GNEP.

This paper proposes an off-line algorithm, called Recurrent Model Predictive Control (RMPC), to solve general nonlinear finite-horizon optimal control problems. Unlike traditional Model Predictive Control (MPC) algorithms, it can make full use of the current computing resources and adaptively select the longest model prediction horizon. Our algorithm employs a recurrent function to approximate the optimal policy, which maps the system states and reference values directly to the control inputs. The number of prediction steps is equal to the number of recurrent cycles of the learned policy function. With an arbitrary initial policy function, the proposed RMPC algorithm can converge to the optimal policy by directly minimizing the designed loss function. We further prove the convergence and optimality of the RMPC algorithm thorough Bellman optimality principle, and demonstrate its generality and efficiency using two numerical examples.

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms can find optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained to predict edges from example solutions. We evaluate our framework on the travelling salesman problem (TSP) and the vehicle routing problem (VRP) and show that the neural policy improves the performance of (restricted) DP algorithms, making them competitive to strong alternatives such as LKH, while also outperforming other `neural approaches' for solving TSPs and VRPs with 100 nodes.

The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the convergence of the stochastic subgradient method for the weakly convex case, which encompasses many important applications (e.g., robust phase retrieval, blind deconvolution, biconvex compressive sensing, and dictionary learning). In practice, distributed implementations of the projected stochastic subgradient method (stoDPSM) are used to speed-up risk minimization. In this paper, we propose a distributed implementation of the stochastic subgradient method with a theoretical guarantee. Specifically, we show the global convergence of stoDPSM using the Moreau envelope stationarity measure. Furthermore, under a so-called sharpness condition, we show that deterministic DPSM (with a proper initialization) converges linearly to the sharp minima, using geometrically diminishing step-size. We provide numerical experiments to support our theoretical analysis.

As quantum computing and networking nodes scale-up, important open questions arise on the causal influence of various sub-systems on the total system performance. These questions are related to the tomographic reconstruction of the macroscopic wavefunction and optimizing connectivity of large engineered qubit systems, the reliable broadcasting of information across quantum networks as well as speed-up of classical causal inference algorithms on quantum computers. A direct generalization of the existing causal inference techniques to the quantum domain is not possible due to superposition and entanglement. We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. First, we build the fundamental connection between the celebrated quantum marginal problem and entropic causal inference. Second, inspired by the definition of geometric quantum discord, we fill the gap between classical conditional probabilities and quantum conditional density matrices. These fundamental theoretical advances are exploited to develop a scalable algorithmic approach for quantum entropic causal inference. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This successful inference on a synthetic quantum dataset can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks. We unify classical and quantum causal inference in a principled way paving the way for future applications in quantum computing and networking.

In recent years, to improve the evolutionary algorithms used to solve optimization problems involving a large number of decision variables, many attempts have been made to simplify the problem solution space of a given problem for the evolutionary search. In the literature, the existing approaches can generally be categorized as decomposition-based methods and dimension-reduction-based methods. The former decomposes a large-scale problem into several smaller subproblems, while the latter transforms the original high-dimensional solution space into a low-dimensional space. However, it is worth noting that a given large-scale optimization problem may not always be decomposable, and it is also difficult to guarantee that the global optimum of the original problem is preserved in the reduced low-dimensional problem space. This paper thus proposes a new search paradigm, namely the multi-space evolutionary search, to enhance the existing evolutionary search methods for solving large-scale optimization problems. In contrast to existing approaches that perform an evolutionary search in a single search space, the proposed paradigm is designed to conduct a search in multiple solution spaces that are derived from the given problem, each possessing a unique landscape. The proposed paradigm makes no assumptions about the large-scale optimization problem of interest, such as that the problem is decomposable or that a certain relationship exists among the decision variables. To verify the efficacy of the proposed paradigm, comprehensive empirical studies in comparison to four state-of-the-art algorithms were conducted using the CEC2013 large-scale benchmark problems.

In 5G Ultra-Dense Networks, a distributed wireless backhaul is an attractive solution for forwarding traffic to the core. The macro-cell coverage area is divided into many small cells. A few of these cells are designated as gateways and are linked to the core by high-capacity fiber optic links. Each small cell is associated with one gateway and all small cells forward their traffic to their respective gateway through multi-hop mesh networks. We investigate the gateway location problem and show that finding near-optimal gateway locations improves the backhaul network capacity. An exact p-median integer linear program is formulated for comparison with our novel K-GA heuristic that combines a Genetic Algorithm (GA) with K-means clustering to find near-optimal gateway locations. We compare the performance of KGA with six other approaches in terms of average number of hops and backhaul network capacity at different node densities through extensive Monte Carlo simulations. All approaches are tested in various user distribution scenarios, including uniform distribution, bivariate Gaussian distribution, and cluster distribution. In all cases K-GA provides near-optimal results, achieving average number of hops and backhaul network capacity within 2% of optimal while saving an average of 95% of the execution time.

We consider the problem of domain generalization, in which a predictor is trained on data drawn from a family of related training domains and tested on a distinct and unseen test domain. While a variety of approaches have been proposed for this setting, it was recently shown that no existing algorithm can consistently outperform empirical risk minimization (ERM) over the training domains. To this end, in this paper we propose a novel approach for the domain generalization problem called Model-Based Domain Generalization. In our approach, we first use unlabeled data from the training domains to learn multi-modal domain transformation models that map data from one training domain to any other domain. Next, we propose a constrained optimization-based formulation for domain generalization which enforces that a trained predictor be invariant to distributional shifts under the underlying domain transformation model. Finally, we propose a novel algorithmic framework for efficiently solving this constrained optimization problem. In our experiments, we show that this approach outperforms both ERM and domain generalization algorithms on numerous well-known, challenging datasets, including WILDS, PACS, and ImageNet. In particular, our algorithms beat the current state-of-the-art methods on the very-recently-proposed WILDS benchmark by up to 20 percentage points.

Cloud computing accelerates design space exploration in logic synthesis, and parameter tuning in physical design. However, deploying EDA jobs on the cloud requires EDA teams to deeply understand the characteristics of their jobs in cloud environments. Unfortunately, there has been little to no public information on these characteristics. Thus, in this paper, we formulate the problem of migrating EDA jobs to the cloud. First, we characterize the performance of four main EDA applications, namely: synthesis, placement, routing and static timing analysis. We show that different EDA jobs require different machine configurations. Second, using observations from our characterization, we propose a novel model based on Graph Convolutional Networks to predict the total runtime of a given application on different machine configurations. Our model achieves a prediction accuracy of 87%. Third, we develop a new formulation for optimizing cloud deployments in order to reduce deployment costs while meeting deadline constraints. We present a pseudo-polynomial optimal solution using a multi-choice knapsack mapping that reduces costs by 35.29%.

Network models provide an efficient way to represent many real life problems mathematically. In the last few decades, the field of network optimization has witnessed an upsurge of interest among researchers and practitioners. The network models considered in this thesis are broadly classified into four types including transportation problem, shortest path problem, minimum spanning tree problem and maximum flow problem. Quite often, we come across situations, when the decision parameters of network optimization problems are not precise and characterized by various forms of uncertainties arising from the factors, like insufficient or incomplete data, lack of evidence, inappropriate judgements and randomness. Considering the deterministic environment, there exist several studies on network optimization problems. However, in the literature, not many investigations on single and multi objective network optimization problems are observed under diverse uncertain frameworks. This thesis proposes seven different network models under different uncertain paradigms. Here, the uncertain programming techniques used to formulate the uncertain network models are (i) expected value model, (ii) chance constrained model and (iii) dependent chance constrained model. Subsequently, the corresponding crisp equivalents of the uncertain network models are solved using different solution methodologies. The solution methodologies used in this thesis can be broadly categorized as classical methods and evolutionary algorithms. The classical methods, used in this thesis, are Dijkstra and Kruskal algorithms, modified rough Dijkstra algorithm, global criterion method, epsilon constraint method and fuzzy programming method. Whereas, among the evolutionary algorithms, we have proposed the varying population genetic algorithm with indeterminate crossover and considered two multi objective evolutionary algorithms.