Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional solvers have had decades to build. We drew inspiration from the warm-start technique used in conventional solvers to address one of the major challenges faced by decision diagram based methods. Decision diagrams become more useful the wider they are allowed to be, but also become more costly to generate, especially with large numbers of variables. In the original version of this paper, we presented a method of peeling off a sub-graph of previously constructed diagrams and using it as the initial diagram for subsequent iterations that we call peel-and-bound. We tested the method on the sequence ordering problem, and our results indicate that our peel-and-bound scheme generates stronger bounds than a branch-and-bound scheme using the same propagators, and at significantly less computational cost. In this extended version of the paper, we also propose new methods for using relaxed decision diagrams to improve the solutions found using restricted decision diagrams, discuss the heuristic decisions involved with the parallelization of peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for sequencing problems. Furthermore, we test the new methods on the sequence ordering problem and the traveling salesman problem with time-windows (TSPTW), and include an updated and generalized implementation of the algorithm capable of handling any discrete optimization problem. The new results show that peel-and-bound outperforms ddo (a decision diagram based branch-and-bound solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.

In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic convex optimization problem. We introduce novel stochastic bilevel optimization methods that locally approximate the solution set of the lower-level problem via a stochastic cutting plane, and then run a conditional gradient update with variance reduction techniques to control the error induced by using stochastic gradients. For the case that the upper-level function is convex, our method requires $\tilde{\mathcal{O}}(\max\{1/\epsilon_f^{2},1/\epsilon_g^{2}\}) $ stochastic oracle queries to obtain a solution that is $\epsilon_f$-optimal for the upper-level and $\epsilon_g$-optimal for the lower-level. This guarantee improves the previous best-known complexity of $\mathcal{O}(\max\{1/\epsilon_f^{4},1/\epsilon_g^{4}\})$. Moreover, for the case that the upper-level function is non-convex, our method requires at most $\tilde{\mathcal{O}}(\max\{1/\epsilon_f^{3},1/\epsilon_g^{3}\}) $ stochastic oracle queries to find an $(\epsilon_f, \epsilon_g)$-stationary point. In the finite-sum setting, we show that the number of stochastic oracle calls required by our method are $\tilde{\mathcal{O}}(\sqrt{n}/\epsilon)$ and $\tilde{\mathcal{O}}(\sqrt{n}/\epsilon^{2})$ for the convex and non-convex settings, respectively, where $\epsilon=\min \{\epsilon_f,\epsilon_g\}$.

As a fundamental problem, numerous methods are dedicated to the optimization of signal-to-interference-plus-noise ratio (SINR), in a multi-user setting. Although traditional model-based optimization methods achieve strong performance, the high complexity raises the research of neural network (NN) based approaches to trade-off the performance and complexity. To fully leverage the high performance of traditional model-based methods and the low complexity of the NN-based method, a knowledge distillation (KD) based algorithm distillation (AD) method is proposed in this paper to improve the performance and convergence speed of the NN-based method, where traditional SINR optimization methods are employed as ``teachers" to assist the training of NNs, which are ``students", thus enhancing the performance of unsupervised and reinforcement learning techniques. This approach aims to alleviate common issues encountered in each of these training paradigms, including the infeasibility of obtaining optimal solutions as labels and overfitting in supervised learning, ensuring higher convergence performance in unsupervised learning, and improving training efficiency in reinforcement learning. Simulation results demonstrate the enhanced performance of the proposed AD-based methods compared to traditional learning methods. Remarkably, this research paves the way for the integration of traditional optimization insights and emerging NN techniques in wireless communication system optimization.

Additionally, new on-demand modalities including ride-share, bike-share, and e-scooters have been introduced in recent years and transformed the transportation landscape in urban environments. A wellfunctioning transit system fosters the growth and expansion of businesses, distributes social and economic benefits, and links the capabilities of community members, thereby enhancing what they can accomplish as a society [6, 11, 15]. However, the explosion in transportation options and the complicated relationship between public and private offerings present myriad new challenges in the design and operation of these systems. There are also complex, and often competing, operational objectives that complicate the implementation of efficient services. Since affordable public transit services are the backbones of many communities, solving these problems and understanding state-of-the-art methods for AI-driven smart transportation has the potential to strengthen urban communities, address the climate challenge, and foster equitable growth. Fundamentally, the design of a well-functioning transit system requires solving complex combinatorial optimization problems related to planning and real-time operations. These problems span many well studied fields, from classical line planning to offline and online vehicle routing problems (VRPs). While there are many ways to assess the performance of smart transportation systems, we largely focus on evaluating these systems in the context of optimizing utilization (i.e.

In recent years, there has been remarkable progress in the development of so-called certifiable perception methods, which leverage semidefinite, convex relaxations to find global optima of perception problems in robotics. However, many of these relaxations rely on simplifying assumptions that facilitate the problem formulation, such as an isotropic measurement noise distribution. In this paper, we explore the tightness of the semidefinite relaxations of matrix-weighted (anisotropic) state-estimation problems and reveal the limitations lurking therein: matrix-weighted factors can cause convex relaxations to lose tightness. In particular, we show that the semidefinite relaxations of localization problems with matrix weights may be tight only for low noise levels. We empirically explore the factors that contribute to this loss of tightness and demonstrate that redundant constraints can be used to regain tightness, albeit at the expense of real-time performance. As a second technical contribution of this paper, we show that the state-of-the-art relaxation of scalar-weighted SLAM cannot be used when matrix weights are considered. We provide an alternate formulation and show that its SDP relaxation is not tight (even for very low noise levels) unless specific redundant constraints are used. We demonstrate the tightness of our formulations on both simulated and real-world data.

Prompt-based pre-trained language models (PLMs) paradigm have succeeded substantially in few-shot natural language processing (NLP) tasks. However, prior discrete prompt optimization methods require expert knowledge to design the base prompt set and identify high-quality prompts, which is costly, inefficient, and subjective. Meanwhile, existing continuous prompt optimization methods improve the performance by learning the ideal prompts through the gradient information of PLMs, whose high computational cost, and low readability and generalizability are often concerning. To address the research gap, we propose a Dialogue-comprised Policy-gradient-based Discrete Prompt Optimization ($DP_2O$) method. We first design a multi-round dialogue alignment strategy for readability prompt set generation based on GPT-4. Furthermore, we propose an efficient prompt screening metric to identify high-quality prompts with linear complexity. Finally, we construct a reinforcement learning (RL) framework based on policy gradients to match the prompts to inputs optimally. By training a policy network with only 0.67% of the PLM parameter size on the tasks in the few-shot setting, $DP_2O$ outperforms the state-of-the-art (SOTA) method by 1.52% in accuracy on average on four open-source datasets. Moreover, subsequent experiments also demonstrate that $DP_2O$ has good universality, robustness, and generalization ability.

Many important real-world problems in different The combination of domain knowledge and centralized scientific fields can be naturally expressed as MaxSAT control is an effective solution to a broad class of optimization [6]: routing and scheduling problems in industrial engineering, problems. However, in the case of complex adaptive systems, software and hardware debugging in computer science and the system's control tends to be distributed and it is often computer engineering, different problems of bioinformatics unclear what the most appropriate trajectory is and even the in biological sciences, just to name a few. It was previously form of the optimal solution may simply be unknown. This is mentioned [7] that the initial weights of the HN network in the case for many kinds of biological systems, but also social an optimization framework represent a weighted-Max-2-SAT systems, that tend to be capable of giving rise to creative problem, but it was never actually shown how one would start solutions even under novel circumstances. Such a complex from a SAT problem in question and use the SO model to solve adaptive system cannot necessarily rely on the availability it (an analogous model to that of SO was used before to solve of error or reward signals to improve its behavior, which a concrete problem [8], but not in the form of a SAT problem raises the intriguing question of what other, more minimal on which we expand subsequently). This poses an obstacle for mechanisms could be available.

Standard bandit algorithms that assume continual reallocation of measurement effort are challenging to implement due to delayed feedback and infrastructural/organizational difficulties. Motivated by practical instances involving a handful of reallocation epochs in which outcomes are measured in batches, we develop a computation-driven adaptive experimentation framework that can flexibly handle batching. Our main observation is that normal approximations, which are universal in statistical inference, can also guide the design of adaptive algorithms. By deriving a Gaussian sequential experiment, we formulate a dynamic program that can leverage prior information on average rewards. Instead of the typical theory-driven paradigm, we leverage computational tools and empirical benchmarking for algorithm development. In particular, our empirical analysis highlights a simple yet effective algorithm, Residual Horizon Optimization, which iteratively solves a planning problem using stochastic gradient descent. Our approach significantly improves statistical power over standard methods, even when compared to Bayesian bandit algorithms (e.g., Thompson sampling) that require full distributional knowledge of individual rewards. Overall, we expand the scope of adaptive experimentation to settings that are difficult for standard methods, involving limited adaptivity, low signal-to-noise ratio, and unknown reward distributions.

In this paper, we consider the closed-loop control problem of nonlinear robotic systems in the presence of probabilistic uncertainties and disturbances. More precisely, we design a state feedback controller that minimizes deviations of the states of the system from the nominal state trajectories due to uncertainties and disturbances. Existing approaches to address the control problem of probabilistic systems are limited to particular classes of uncertainties and systems such as Gaussian uncertainties and processes and linearized systems. We present an approach that deals with nonlinear dynamics models and arbitrary known probabilistic uncertainties. We formulate the controller design problem as an optimization problem in terms of statistics of the probability distributions including moments and characteristic functions. In particular, in the provided optimization problem, we use moments and characteristic functions to propagate uncertainties throughout the nonlinear motion model of robotic systems. In order to reduce the tracking deviations, we minimize the uncertainty of the probabilistic states around the nominal trajectory by minimizing the trace and the determinant of the covariance matrix of the probabilistic states. To obtain the state feedback gains, we solve deterministic optimization problems in terms of moments, characteristic functions, and state feedback gains using off-the-shelf interior-point optimization solvers. To illustrate the performance of the proposed method, we compare our method with existing probabilistic control methods.

We present the OMG-CMDP! algorithm for regret minimization in adversarial Contextual MDPs. The algorithm operates under the minimal assumptions of realizable function class and access to online least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient online regression oracles), simple and robust to approximation errors. It enjoys an $\widetilde{O}(H^{2.5} \sqrt{ T|S||A| ( \mathcal{R}(\mathcal{O}) + H \log(\delta^{-1}) )})$ regret guarantee, with $T$ being the number of episodes, $S$ the state space, $A$ the action space, $H$ the horizon and $\mathcal{R}(\mathcal{O}) = \mathcal{R}(\mathcal{O}_{\mathrm{sq}}^\mathcal{F}) + \mathcal{R}(\mathcal{O}_{\mathrm{log}}^\mathcal{P})$ is the sum of the regression oracles' regret, used to approximate the context-dependent rewards and dynamics, respectively. To the best of our knowledge, our algorithm is the first efficient rate optimal regret minimization algorithm for adversarial CMDPs that operates under the minimal standard assumption of online function approximation.