Graph learning from signals is a core task in Graph Signal Processing (GSP). One of the most commonly used models to learn graphs from stationary signals is SpecT. However, its practical formulation rSpecT is known to be sensitive to hyperparameter selection and, even worse, to suffer from infeasibility. In this paper, we give the first condition that guarantees the infeasibility of rSpecT and design a novel model (LogSpecT) and its practical formulation (rLogSpecT) to overcome this issue. Contrary to rSpecT, the novel practical model rLogSpecT is always feasible. Furthermore, we provide recovery guarantees of rLogSpecT, which are derived from modern optimization tools related to epi-convergence. These tools could be of independent interest and significant for various learning problems. To demonstrate the advantages of rLogSpecT in practice, a highly efficient algorithm based on the linearized alternating direction method of multipliers (L-ADMM) is proposed. The subproblems of L-ADMM admit closed-form solutions and the convergence is guaranteed. Extensive numerical results on both synthetic and real networks corroborate the stability and superiority of our proposed methods, underscoring their potential for various graph learning applications.

We focus on an online 2-stage problem, motivated by the following situation: consider a system where students shall be assigned to universities. There is a first round where some students apply, and a first (stable) matching $M_1$ has to be computed. However, some students may decide to leave the system (change their plan, go to a foreign university, or to some institution not in the system). Then, in a second round (after these deletions), we shall compute a second (final) stable matching $M_2$. As it is undesirable to change assignments, the goal is to minimize the number of divorces/modifications between the two stable matchings $M_1$ and $M_2$. Then, how should we choose $M_1$ and $M_2$? We show that there is an {\it optimal online} algorithm to solve this problem. In particular, thanks to a dominance property, we show that we can optimally compute $M_1$ without knowing the students that will leave the system. We generalize the result to some other possible modifications in the input (students, open positions). We also tackle the case of more stages, showing that no competitive (online) algorithm can be achieved for the considered problem as soon as there are 3 stages.

This paper presents a decentralized multi-agent trajectory planning (MATP) algorithm that guarantees to generate a safe, deadlock-free trajectory in an obstacle-rich environment under a limited communication range. The proposed algorithm utilizes a grid-based multi-agent path planning (MAPP) algorithm for deadlock resolution, and we introduce the subgoal optimization method to make the agent converge to the waypoint generated from the MAPP without deadlock. In addition, the proposed algorithm ensures the feasibility of the optimization problem and collision avoidance by adopting a linear safe corridor (LSC). We verify that the proposed algorithm does not cause a deadlock in both random forests and dense mazes regardless of communication range, and it outperforms our previous work in flight time and distance. We validate the proposed algorithm through a hardware demonstration with ten quadrotors.

Adaptive machines have the potential to assist or interfere with human behavior in a range of contexts, from cognitive decision-making to physical device assistance. Therefore it is critical to understand how machine learning algorithms can influence human actions, particularly in situations where machine goals are misaligned with those of people. Since humans continually adapt to their environment using a combination of explicit and implicit strategies, when the environment contains an adaptive machine, the human and machine play a game. Game theory is an established framework for modeling interactions between two or more decision-makers that has been applied extensively in economic markets and machine algorithms. However, existing approaches make assumptions about, rather than empirically test, how adaptation by individual humans is affected by interaction with an adaptive machine. Here we tested learning algorithms for machines playing general-sum games with human subjects. Our algorithms enable the machine to select the outcome of the co-adaptive interaction from a constellation of game-theoretic equilibria in action and policy spaces. Importantly, the machine learning algorithms work directly from observations of human actions without solving an inverse problem to estimate the human's utility function as in prior work. Surprisingly, one algorithm can steer the human-machine interaction to the machine's optimum, effectively controlling the human's actions even while the human responds optimally to their perceived cost landscape. Our results show that game theory can be used to predict and design outcomes of co-adaptive interactions between intelligent humans and machines.

With the slowdown of improvement in conventional von Neumann systems, increasing attention is paid to novel paradigms such as Ising machines. They have very different approach to NP-complete optimization problems. Ising machines have shown great potential in solving binary optimization problems like MaxCut. In this paper, we present an analysis of these systems in satisfiability (SAT) problems. We demonstrate that, in the case of 3-SAT, a basic architecture fails to produce meaningful acceleration, thanks in no small part to the relentless progress made in conventional SAT solvers. Nevertheless, careful analysis attributes part of the failure to the lack of two important components: cubic interactions and efficient randomization heuristics. To overcome these limitations, we add proper architectural support for cubic interaction on a state-of-the-art Ising machine. More importantly, we propose a novel semantic-aware annealing schedule that makes the search-space navigation much more efficient than existing annealing heuristics. With experimental analyses, we show that such an Augmented Ising Machine for SAT (AIMS), outperforms state-of-the-art software-based, GPU-based and conventional hardware SAT solvers by orders of magnitude. We also demonstrate AIMS to be relatively robust against device variation and noise.

When solving global optimization problems in practice, one often ends up repeatedly solving problems that are similar to each others. By providing a rigorous definition of similarity, in this work we propose to incorporate the META-learning rationale into SMGO-$\Delta$, a global optimization approach recently proposed in the literature, to exploit priors obtained from similar past experience to efficiently solve new (similar) problems. Through a benchmark numerical example we show the practical benefits of our META-extension of the baseline algorithm, while providing theoretical bounds on its performance.

Genetic Algorithm (GA) is a popular meta-heuristic evolutionary algorithm that uses stochastic operators to find optimal solution and has proved its effectiveness in solving many complex optimization problems (such as classification, optimization, and scheduling). However, despite its performance, popularity and simplicity, not much attention has been paid towards reproducibility and reusability of GA. In this paper, we have extended Findable, Accessible, Interoperable and Reusable (FAIR) data principles to enable the reproducibility and reusability of algorithms. We have chosen GA as a usecase to the demonstrate the applicability of the proposed principles. Also we have presented an overview of methodological developments and variants of GA that makes it challenging to reproduce or even find the right source. Additionally, to enable FAIR algorithms, we propose a vocabulary (i.e. $evo$) using light weight RDF format, facilitating the reproducibility. Given the stochastic nature of GAs, this work can be extended to numerous Optimization and machine learning algorithms/methods.

Many re-ranking strategies in search systems rely on stochastic ranking policies, encoded as Doubly-Stochastic (DS) matrices, that satisfy desired ranking constraints in expectation, e.g., Fairness of Exposure (FOE). These strategies are generally two-stage pipelines: \emph{i)} an offline re-ranking policy construction step and \emph{ii)} an online sampling of rankings step. Building a re-ranking policy requires repeatedly solving a constrained optimization problem, one for each issued query. Thus, it is necessary to recompute the optimization procedure for any new/unseen query. Regarding sampling, the Birkhoff-von-Neumann decomposition (BvND) is the favored approach to draw rankings from any DS-based policy. However, the BvND is too costly to compute online. Hence, the BvND as a sampling solution is memory-consuming as it can grow as $\gO(N\, n^2)$ for $N$ queries and $n$ documents. This paper offers a novel, fast, lightweight way to predict fair stochastic re-ranking policies: Constrained Meta-Optimal Transport (CoMOT). This method fits a neural network shared across queries like a learning-to-rank system. We also introduce Gumbel-Matching Sampling (GumMS), an online sampling approach from DS-based policies. Our proposed pipeline, CoMOT + GumMS, only needs to store the parameters of a single model, and it generalizes to unseen queries. We empirically evaluated our pipeline on the TREC 2019 and 2020 datasets under FOE constraints. Our experiments show that CoMOT rapidly predicts fair re-ranking policies on held-out data, with a speed-up proportional to the average number of documents per query. It also displays fairness and ranking performance similar to the original optimization-based policy. Furthermore, we empirically validate the effectiveness of GumMS to approximate DS-based policies in expectation.

Generally, system operators conduct the economic operation of power systems in an open-loop predict-then-optimize process: the renewable energy source (RES) availability and system reserve requirements are first predicted; given the predictions, system operators solve optimization models such as unit commitment (UC) to determine the economical operation plans accordingly. However, such an open-loop process could essentially compromise the operation economics because its predictors myopically seek to improve the immediate statistical prediction errors instead of the ultimate operation cost. To this end, this paper presents a closed-loop predict-and-optimize framework, offering a prescriptive UC to improve the operation economics. First, a bilevel mixed-integer programming model is leveraged to train cost-oriented predictors tailored for optimal system operations: the upper level trains the RES and reserve predictors based on their induced operation cost; the lower level, with given predictions, mimics the system operation process and feeds the induced operation cost back to the upper level. Furthermore, the embeddability of the trained predictors grants a prescriptive UC model, which simultaneously provides RES-reserve predictions and UC decisions with enhanced operation economics. Finally, numerical case studies using real-world data illustrate the potential economic and practical advantages of prescriptive UC over deterministic, robust, and stochastic UC models.

Large language models show impressive results at predicting structured text such as code, but also commonly introduce errors and hallucinations in their output. When used to assist software developers, these models may make mistakes that users must go back and fix, or worse, introduce subtle bugs that users may miss entirely. We propose Randomized Utility-driven Synthesis of Uncertain REgions (R-U-SURE), an approach for building uncertainty-aware suggestions based on a decision-theoretic model of goal-conditioned utility, using random samples from a generative model as a proxy for the unobserved possible intents of the end user. Our technique combines minimum-Bayes-risk decoding, dual decomposition, and decision diagrams in order to efficiently produce structured uncertainty summaries, given only sample access to an arbitrary generative model of code and an optional AST parser. We demonstrate R-U-SURE on three developer-assistance tasks, and show that it can be applied different user interaction patterns without retraining the model and leads to more accurate uncertainty estimates than token-probability baselines. We also release our implementation as an open-source library at https://github.com/google-research/r_u_sure.