Mixed integer problems are ubiquitous in decision making, from discrete device settings and design parameters, unit production, and on/off or yes/no decision in switches, routing, and social networks. Despite their prevalence, classical optimization approaches for combinatorial optimization remain prohibitively slow for fast and accurate decision making in dynamic and safety-critical environments with hard constraints. To address this gap, we propose SiPhyR (pronounced: cipher), a physics-informed machine learning framework for end-to-end learning to optimize for combinatorial problems. SiPhyR employs a novel physics-informed rounding approach to tackle the challenge of combinatorial optimization within a differentiable framework that has certified satisfiability of safety-critical constraints. We demonstrate the effectiveness of SiPhyR on an emerging paradigm for clean energy systems: dynamic reconfiguration, where the topology of the electric grid and power flow are optimized so as to maintain a safe and reliable power grid in the presence of intermittent renewable generation. Offline training of the unsupervised framework on representative load and generation data makes dynamic decision making via the online application of Grid-SiPhyR computationally feasible.

Previous work on controllable text generation has explored the idea of control from the latent space, such as optimizing a representation with attribute-related classifiers or sampling a representation from relevant discrete samples. However, they are not effective enough in modeling both the latent space and the control, leaving controlled text with low quality and diversity. In this work, we propose a novel control framework using probability density estimation in the latent space. Our method utilizes an invertible transformation function, the Normalizing Flow, that maps the complex distributions in the latent space to simple Gaussian distributions in the prior space. Thus, we can perform sophisticated and flexible control in the prior space and feed the control effects back into the latent space owing to the one-one-mapping property of invertible transformations. Experiments on single-attribute controls and multi-attribute control reveal that our method outperforms several strong baselines on attribute relevance and text quality and achieves the SOTA. Further analysis of control strength adjustment demonstrates the flexibility of our control strategy.

We investigate the convergence of stochastic mirror descent (SMD) under interpolation in relatively smooth and smooth convex optimization. In relatively smooth convex optimization we provide new convergence guarantees for SMD with a constant stepsize. For smooth convex optimization we propose a new adaptive stepsize scheme -- the mirror stochastic Polyak stepsize (mSPS). Notably, our convergence results in both settings do not make bounded gradient assumptions or bounded variance assumptions, and we show convergence to a neighborhood that vanishes under interpolation. Consequently, these results correspond to the first convergence guarantees under interpolation for the exponentiated gradient algorithm for fixed or adaptive stepsizes. mSPS generalizes the recently proposed stochastic Polyak stepsize (SPS) (Loizou et al. 2021) to mirror descent and remains both practical and efficient for modern machine learning applications while inheriting the benefits of mirror descent. We complement our results with experiments across various supervised learning tasks and different instances of SMD, demonstrating the effectiveness of mSPS.

Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as a conditional generative modelling problem, where a large generative model over protein sequences is conditioned on the backbone. While these generative models very rapidly produce promising sequences, independent draws from generative models may fail to produce sequences that reliably fold to the correct backbone. Furthermore, it is challenging to adapt pure generative approaches to other settings, e.g., when constraints exist. In this paper, we cast the problem of improving generated inverse folds as an optimization problem that we solve using recent advances in "deep" or "latent space" Bayesian optimization. Our approach consistently produces protein sequences with greatly reduced structural error to the target backbone structure as measured by TM score and RMSD while using fewer computational resources. Additionally, we demonstrate other advantages of an optimization-based approach to the problem, such as the ability to handle constraints.

Task allocation can enable effective coordination of multi-robot teams to accomplish tasks that are intractable for individual robots. However, existing approaches to task allocation often assume that task requirements or reward functions are known and explicitly specified by the user. In this work, we consider the challenge of forming effective coalitions for a given heterogeneous multi-robot team when task reward functions are unknown. To this end, we first formulate a new class of problems, dubbed COncurrent Constrained Online optimization of Allocation (COCOA). The COCOA problem requires online optimization of coalitions such that the unknown rewards of all the tasks are simultaneously maximized using a given multi-robot team with constrained resources. To address the COCOA problem, we introduce an online optimization algorithm, named Concurrent Multi-Task Adaptive Bandits (CMTAB), that leverages and builds upon continuum-armed bandit algorithms. Experiments involving detailed numerical simulations and a simulated emergency response task reveal that CMTAB can effectively trade-off exploration and exploitation to simultaneously and efficiently optimize the unknown task rewards while respecting the team's resource constraints.

Since acquiring perfect supervision is usually difficult, real-world machine learning tasks often confront inaccurate, incomplete, or inexact supervision, collectively referred to as weak supervision. In this work, we present WSAUC, a unified framework for weakly supervised AUC optimization problems, which covers noisy label learning, positive-unlabeled learning, multi-instance learning, and semi-supervised learning scenarios. Within the WSAUC framework, we first frame the AUC optimization problems in various weakly supervised scenarios as a common formulation of minimizing the AUC risk on contaminated sets, and demonstrate that the empirical risk minimization problems are consistent with the true AUC. Then, we introduce a new type of partial AUC, specifically, the reversed partial AUC (rpAUC), which serves as a robust training objective for AUC maximization in the presence of contaminated labels. WSAUC offers a universal solution for AUC optimization in various weakly supervised scenarios by maximizing the empirical rpAUC. Theoretical and experimental results under multiple settings support the effectiveness of WSAUC on a range of weakly supervised AUC optimization tasks.

The problem of constrained reinforcement learning (CRL) holds significant importance as it provides a framework for addressing critical safety satisfaction concerns in the field of reinforcement learning (RL). However, with the introduction of constraint satisfaction, the current CRL methods necessitate the utilization of second-order optimization or primal-dual frameworks with additional Lagrangian multipliers, resulting in increased complexity and inefficiency during implementation. To address these issues, we propose a novel first-order feasible method named Constrained Proximal Policy Optimization (CPPO). By treating the CRL problem as a probabilistic inference problem, our approach integrates the Expectation-Maximization framework to solve it through two steps: 1) calculating the optimal policy distribution within the feasible region (E-step), and 2) conducting a first-order update to adjust the current policy towards the optimal policy obtained in the E-step (M-step). We establish the relationship between the probability ratios and KL divergence to convert the E-step into a convex optimization problem. Furthermore, we develop an iterative heuristic algorithm from a geometric perspective to solve this problem. Additionally, we introduce a conservative update mechanism to overcome the constraint violation issue that occurs in the existing feasible region method. Empirical evaluations conducted in complex and uncertain environments validate the effectiveness of our proposed method, as it performs at least as well as other baselines.

Software built on top of machine learning algorithms is becoming increasingly prevalent in a variety of fields, including college admissions, healthcare, insurance, and justice. The effectiveness and efficiency of these systems heavily depend on the quality of the training datasets. Biased datasets can lead to unfair and potentially harmful outcomes, particularly in such critical decision-making systems where the allocation of resources may be affected. This can exacerbate discrimination against certain groups and cause significant social disruption. To mitigate such unfairness, a series of bias-mitigating methods are proposed. Generally, these studies improve the fairness of the trained models to a certain degree but with the expense of sacrificing the model performance. In this paper, we propose FITNESS, a bias mitigation approach via de-correlating the causal effects between sensitive features (e.g., the sex) and the label. Our key idea is that by de-correlating such effects from a causality perspective, the model would avoid making predictions based on sensitive features and thus fairness could be improved. Furthermore, FITNESS leverages multi-objective optimization to achieve a better performance-fairness trade-off. To evaluate the effectiveness, we compare FITNESS with 7 state-of-the-art methods in 8 benchmark tasks by multiple metrics. Results show that FITNESS can outperform the state-of-the-art methods on bias mitigation while preserve the model's performance: it improved the model's fairness under all the scenarios while decreased the model's performance under only 26.67% of the scenarios. Additionally, FITNESS surpasses the Fairea Baseline in 96.72% cases, outperforming all methods we compared.

We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We characterize the maximum possible value of the supermodular rank and describe the functions with fixed supermodular rank. We analogously define the submodular rank. We use submodular decompositions to optimize set functions. Given a bound on the submodular rank of a set function, we formulate an algorithm that splits an optimization problem into submodular subproblems. We show that this method improves the approximation ratio guarantees of several algorithms for monotone set function maximization and ratio of set functions minimization, at a computation overhead that depends on the submodular rank.

Ke Wan, Zuo Zhang and Zhiquan Chen are with the Department of Automation, Tsinghua University, Beijing 100084, P.R.China. ABSTRACT Dynamic traffic assignment and vehicle route guidance have been important problems in ITS for some time. This paper proposes a new model for VRGS, which takes into consideration of the information propagation, user selection and information reaction. Parameter p is then defined as the updating weight for computing cost of traffic based on a distributive learning scheme. Comparison to static traffic assignment, DTA and feasible strategies are given, and future work is also stated.