In settings such as e-recruitment and online dating, recommendation involves distributing limited opportunities, calling for novel approaches to quantify and enforce fairness. We introduce \emph{inferiority}, a novel (un)fairness measure quantifying a user's competitive disadvantage for their recommended items. Inferiority complements \emph{envy}, a fairness notion measuring preference for others' recommendations. We combine inferiority and envy with \emph{utility}, an accuracy-related measure of aggregated relevancy scores. Since these measures are non-differentiable, we reformulate them using a probabilistic interpretation of recommender systems, yielding differentiable versions. We combine these loss functions in a multi-objective optimization problem called \texttt{FEIR} (Fairness through Envy and Inferiority Reduction), applied as post-processing for standard recommender systems. Experiments on synthetic and real-world data demonstrate that our approach improves trade-offs between inferiority, envy, and utility compared to naive recommendations and the baseline methods.

Bayesian Optimization (BO), guided by Gaussian process (GP) surrogates, has proven to be an invaluable technique for efficient, high-dimensional, black-box optimization, a critical problem inherent to many applications such as industrial design and scientific computing. Recent contributions have introduced reinforcement learning (RL) to improve the optimization performance on both single function optimization and \textit{few-shot} multi-objective optimization. However, even few-shot techniques fail to exploit similarities shared between closely related objectives. In this paper, we combine recent developments in Deep Kernel Learning (DKL) and attention-based Transformer models to improve the modeling powers of GP surrogates with meta-learning. We propose a novel method for improving meta-learning BO surrogates by incorporating attention mechanisms into DKL, empowering the surrogates to adapt to contextual information gathered during the BO process. We combine this Transformer Deep Kernel with a learned acquisition function trained with continuous Soft Actor-Critic Reinforcement Learning to aid in exploration. This Reinforced Transformer Deep Kernel (RTDK-BO) approach yields state-of-the-art results in continuous high-dimensional optimization problems.

Policy-Space Response Oracles (PSRO) is an influential algorithm framework for approximating a Nash Equilibrium (NE) in multi-agent non-transitive games. Many previous studies have been trying to promote policy diversity in PSRO. A major weakness in existing diversity metrics is that a more diverse (according to their diversity metrics) population does not necessarily mean (as we proved in the paper) a better approximation to a NE. To alleviate this problem, we propose a new diversity metric, the improvement of which guarantees a better approximation to a NE. Meanwhile, we develop a practical and well-justified method to optimize our diversity metric using only state-action samples. By incorporating our diversity regularization into the best response solving in PSRO, we obtain a new PSRO variant, Policy Space Diversity PSRO (PSD-PSRO). We present the convergence property of PSD-PSRO. Empirically, extensive experiments on various games demonstrate that PSD-PSRO is more effective in producing significantly less exploitable policies than state-of-the-art PSRO variants.

Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems. However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and discrete number of subsets is inherently non-differentiable, prohibiting end-to-end gradient-based optimization of parameters. We overcome this limitation by proposing a novel two-step method for inferring partitions, which allows its usage in variational inference tasks. This new approach enables reparameterized gradients with respect to the parameters of the new random partition model. Our method works by inferring the number of elements per subset and, second, by filling these subsets in a learned order. We highlight the versatility of our general-purpose approach on three different challenging experiments: variational clustering, inference of shared and independent generative factors under weak supervision, and multitask learning.

Designing and analyzing model-based RL (MBRL) algorithms with guaranteed monotonic improvement has been challenging, mainly due to the interdependence between policy optimization and model learning. Existing discrepancy bounds generally ignore the impacts of model shifts, and their corresponding algorithms are prone to degrade performance by drastic model updating. In this work, we first propose a novel and general theoretical scheme for a non-decreasing performance guarantee of MBRL. Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. These discoveries encourage us to formulate a constrained lower-bound optimization problem to permit the monotonicity of MBRL. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns. Motivated by these analyses, we design a simple but effective algorithm CMLO (Constrained Model-shift Lower-bound Optimization), by introducing an event-triggered mechanism that flexibly determines when to update the model. Experiments show that CMLO surpasses other state-of-the-art methods and produces a boost when various policy optimization methods are employed.

We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set. For this setup, we propose a novel decentralized algorithm, called DAGP (Double Averaging and Gradient Projection), based on local gradients, projection onto local constraints, and local averaging. We achieve global optimality through a novel distributed tracking technique we call distributed null projection. Further, we show that DAGP can be used to solve unconstrained problems with non-differentiable objective terms with a problem reduction scheme. Assuming only smoothness of the objective terms, we study the convergence of DAGP and establish sub-linear rates of convergence in terms of feasibility, consensus, and optimality, with no extra assumption (e.g. strong convexity). For the analysis, we forego the difficulties of selecting Lyapunov functions by proposing a new methodology of convergence analysis in optimization problems, which we refer to as aggregate lower-bounding. To demonstrate the generality of this method, we also provide an alternative convergence proof for the standard gradient descent algorithm with smooth functions. Finally, we present numerical results demonstrating the effectiveness of our proposed method in both constrained and unconstrained problems. In particular, we propose a distributed scheme by DAGP for the optimal transport problem with superior performance and speed.

Optimization problems on manifolds are ubiquitous in science and engineering. For instance, lowrank matrix completion and rotational alignment of 3D bodies can be formulated as optimization problems over spaces of matrices that are naturally endowed with manifold structures. These matrix manifolds belong to agreeable families [56] for which Riemannian gradients, geodesics, and other geometric quantities have closed-form expressions that facilitate the use of Riemannian optimization algorithms [19, 1, 9]. In contrast, this paper is motivated by optimization problems where the search space is a manifold that the practitioner can only access through a discrete point cloud representation, preventing direct use of Riemannian optimization algorithms. Moreover, the hidden manifold may not belong to an agreeable family, further hindering the use of classical methods. Illustrative examples where manifolds are represented by point cloud data include computer vision, robotics, and shape analysis of geometric morphometrics [33, 23, 25]. Additionally, across many applications in data science, high-dimensional point cloud data contains low-dimensional structure that can be modeled as a manifold for algorithmic design and theoretical analysis [14, 3, 27]. Motivated by these problems, this paper introduces a Bayesian optimization method with convergence guarantees to optimize an expensive-to-evaluate function on a point cloud of manifold samples.

Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process. Cover-encoding maps were devised to circumvent this problem by transforming the original landscape to one that is free of local minima and enriched in near-optimal solutions. By definition, these involve the mapping of the original (larger) search space into smaller subspaces, by processes that typically amount to a form of coarse-graining. In this paper, we explore the details of this coarse-graining using formal arguments, as well as concrete examples of cover-encoding maps, that are investigated analytically as well as computationally. Our results strongly suggest that the coarse-graining involved in cover-encoding maps bears a strong resemblance to that encountered in renormalisation group schemes. Given the apparently disparate nature of these two formalisms, these strong similarities are rather startling, and suggest deep mathematical underpinnings that await further exploration.

The evolution of wireless mobile networks towards cloudification, where Radio Access Network (RAN) functions can be hosted at either a central or distributed locations, offers many benefits like low cost deployment, higher capacity, and improved hardware utilization. Nevertheless, the flexibility in the functional deployment comes at the cost of stringent fronthaul (FH) capacity and latency requirements. One possible approach to deal with these rigorous constraints is to use FH compression techniques. To ensure that FH capacity and latency requirements are met, more FH compression is applied during high load, while less compression is applied during medium and low load to improve FH utilization and air interface performance. In this paper, a model-free deep reinforcement learning (DRL) based FH compression (DRL-FC) framework is proposed that dynamically controls FH compression through various configuration parameters such as modulation order, precoder granularity, and precoder weight quantization that affect both FH load and air interface performance. Simulation results show that DRL-FC exhibits significantly higher FH utilization (68.7% on average) and air interface throughput than a reference scheme (i.e. with no applied compression) across different FH load levels. At the same time, the proposed DRL-FC framework is able to meet the predefined FH latency constraints (in our case set to 260 $\mu$s) under various FH loads.

Robot-assisted dressing could profoundly enhance the quality of life of adults with physical disabilities. To achieve this, a robot can benefit from both visual and force sensing. The former enables the robot to ascertain human body pose and garment deformations, while the latter helps maintain safety and comfort during the dressing process. In this paper, we introduce a new technique that leverages both vision and force modalities for this assistive task. Our approach first trains a vision-based dressing policy using reinforcement learning in simulation with varying body sizes, poses, and types of garments. We then learn a force dynamics model for action planning to ensure safety. Due to limitations of simulating accurate force data when deformable garments interact with the human body, we learn a force dynamics model directly from real-world data. Our proposed method combines the vision-based policy, trained in simulation, with the force dynamics model, learned in the real world, by solving a constrained optimization problem to infer actions that facilitate the dressing process without applying excessive force on the person. We evaluate our system in simulation and in a real-world human study with 10 participants across 240 dressing trials, showing it greatly outperforms prior baselines. Video demonstrations are available on our project website\footnote{\url{https://sites.google.com/view/dressing-fcvp}}.