Efficiently allocating treatments with a budget constraint constitutes an important challenge across various domains. In marketing, for example, the use of promotions to target potential customers and boost conversions is limited by the available budget. While much research focuses on estimating causal effects, there is relatively limited work on learning to allocate treatments while considering the operational context. Existing methods for uplift modeling or causal inference primarily estimate treatment effects, without considering how this relates to a profit maximizing allocation policy that respects budget constraints. The potential downside of using these methods is that the resulting predictive model is not aligned with the operational context. Therefore, prediction errors are propagated to the optimization of the budget allocation problem, subsequently leading to a suboptimal allocation policy. We propose an alternative approach based on learning to rank. Our proposed methodology directly learns an allocation policy by prioritizing instances in terms of their incremental profit. We propose an efficient sampling procedure for the optimization of the ranking model to scale our methodology to large-scale data sets. Theoretically, we show how learning to rank can maximize the area under a policy's incremental profit curve. Empirically, we validate our methodology and show its effectiveness in practice through a series of experiments on both synthetic and real-world data.

We present X-SLAM, a real-time dense differentiable SLAM system that leverages the complex-step finite difference (CSFD) method for efficient calculation of numerical derivatives, bypassing the need for a large-scale computational graph. The key to our approach is treating the SLAM process as a differentiable function, enabling the calculation of the derivatives of important SLAM parameters through Taylor series expansion within the complex domain. Our system allows for the real-time calculation of not just the gradient, but also higher-order differentiation. This facilitates the use of high-order optimizers to achieve better accuracy and faster convergence. Building on X-SLAM, we implemented end-to-end optimization frameworks for two important tasks: camera relocalization in wide outdoor scenes and active robotic scanning in complex indoor environments. Comprehensive evaluations on public benchmarks and intricate real scenes underscore the improvements in the accuracy of camera relocalization and the efficiency of robotic navigation achieved through our task-aware optimization. The code and data are available at https://gapszju.github.io/X-SLAM.

Computed Tomography (CT) is pivotal in industrial quality control and medical diagnostics. Sparse-view CT, offering reduced ionizing radiation, faces challenges due to its under-sampled nature, leading to ill-posed reconstruction problems. Recent advancements in Implicit Neural Representations (INRs) have shown promise in addressing sparse-view CT reconstruction. Recognizing that CT often involves scanning similar subjects, we propose a novel approach to improve reconstruction quality through joint reconstruction of multiple objects using INRs. This approach can potentially leverage both the strengths of INRs and the statistical regularities across multiple objects. While current INR joint reconstruction techniques primarily focus on accelerating convergence via meta-initialization, they are not specifically tailored to enhance reconstruction quality. To address this gap, we introduce a novel INR-based Bayesian framework integrating latent variables to capture the inter-object relationships. These variables serve as a dynamic reference throughout the optimization, thereby enhancing individual reconstruction fidelity. Our extensive experiments, which assess various key factors such as reconstruction quality, resistance to overfitting, and generalizability, demonstrate significant improvements over baselines in common numerical metrics. This underscores a notable advancement in CT reconstruction methods.

Multi-task reinforcement learning (RL) aims to find a single policy that effectively solves multiple tasks at the same time. This paper presents a constrained formulation for multi-task RL where the goal is to maximize the average performance of the policy across tasks subject to bounds on the performance in each task. We consider solving this problem both in the centralized setting, where information for all tasks is accessible to a single server, and in the decentralized setting, where a network of agents, each given one task and observing local information, cooperate to find the solution of the globally constrained objective using local communication. We first propose a primal-dual algorithm that provably converges to the globally optimal solution of this constrained formulation under exact gradient evaluations. When the gradient is unknown, we further develop a sampled-based actor-critic algorithm that finds the optimal policy using online samples of state, action, and reward. Finally, we study the extension of the algorithm to the linear function approximation setting.

This paper studies an online optimal resource reservation problem in communication networks with job transfers where the goal is to minimize the reservation cost while maintaining the blocking cost under a certain budget limit. To tackle this problem, we propose a novel algorithm based on a randomized exponentially weighted method that encompasses long-term constraints. We then analyze the performance of our algorithm by establishing an upper bound for the associated regret and the cumulative constraint violations. Finally, we present numerical experiments where we compare the performance of our algorithm with those of reinforcement learning where we show that our algorithm surpasses it.

Experimental design techniques such as active search and Bayesian optimization are widely used in the natural sciences for data collection and discovery. However, existing techniques tend to favor exploitation over exploration of the search space, which causes them to get stuck in local optima. This ``collapse" problem prevents experimental design algorithms from yielding diverse high-quality data. In this paper, we extend the Vendi scores -- a family of interpretable similarity-based diversity metrics -- to account for quality. We then leverage these quality-weighted Vendi scores to tackle experimental design problems across various applications, including drug discovery, materials discovery, and reinforcement learning. We found that quality-weighted Vendi scores allow us to construct policies for experimental design that flexibly balance quality and diversity, and ultimately assemble rich and diverse sets of high-performing data points. Our algorithms led to a 70%-170% increase in the number of effective discoveries compared to baselines.

Robotic applications across industries demand advanced navigation for safe and smooth movement. Smooth path planning is crucial for mobile robots to ensure stable and efficient navigation, as it minimizes jerky movements and enhances overall performance Achieving this requires smooth collision-free paths. Partial Swarm Optimization (PSO) and Potential Field (PF) are notable path-planning techniques, however, they may struggle to produce smooth paths due to their inherent algorithms, potentially leading to suboptimal robot motion and increased energy consumption. In addition, while PSO efficiently explores solution spaces, it generates long paths and has limited global search. On the contrary, PF methods offer concise paths but struggle with distant targets or obstacles. To address this, we propose Smoothed Partial Swarm Optimization with Improved Potential Field (SPSO-IPF), combining both approaches and it is capable of generating a smooth and safe path. Our research demonstrates SPSO-IPF's superiority, proving its effectiveness in static and dynamic environments compared to a mere PSO or a mere PF approach.

Deformable object manipulation is a long-standing challenge in robotics. While existing approaches often focus narrowly on a specific type of object, we seek a general-purpose algorithm, capable of manipulating many different types of objects: beans, rope, cloth, liquid, . . . . One key difficulty is a suitable representation, rich enough to capture object shape, dynamics for manipulation and yet simple enough to be acquired effectively from sensor data. Specifically, we propose Differentiable Particles (DiPac), a new algorithm for deformable object manipulation. DiPac represents a deformable object as a set of particles and uses a differentiable particle dynamics simulator to reason about robot manipulation. To find the best manipulation action, DiPac combines learning, planning, and trajectory optimization through differentiable trajectory tree optimization. Differentiable dynamics provides significant benefits and enable DiPac to (i) estimate the dynamics parameters efficiently, thereby narrowing the sim-to-real gap, and (ii) choose the best action by backpropagating the gradient along sampled trajectories. Both simulation and real-robot experiments show promising results. DiPac handles a variety of object types. By combining planning and learning, DiPac outperforms both pure model-based planning methods and pure data-driven learning methods. In addition, DiPac is robust and adapts to changes in dynamics, thereby enabling the transfer of an expert policy from one object to another with different physical properties, e.g., from a rigid rod to a deformable rope.

As a generalization of graphs, hypergraphs are widely used to model higher-order relations in data. This paper explores the benefit of the hypergraph structure for the interpolation of point cloud data that contain no explicit structural information. We define the $\varepsilon_n$-ball hypergraph and the $k_n$-nearest neighbor hypergraph on a point cloud and study the $p$-Laplacian regularization on the hypergraphs. We prove the variational consistency between the hypergraph $p$-Laplacian regularization and the continuum $p$-Laplacian regularization in a semisupervised setting when the number of points $n$ goes to infinity while the number of labeled points remains fixed. A key improvement compared to the graph case is that the results rely on weaker assumptions on the upper bound of $\varepsilon_n$ and $k_n$. To solve the convex but non-differentiable large-scale optimization problem, we utilize the stochastic primal-dual hybrid gradient algorithm. Numerical experiments on data interpolation verify that the hypergraph $p$-Laplacian regularization outperforms the graph $p$-Laplacian regularization in preventing the development of spikes at the labeled points.

Recently, there has been an increasing interest in exploring the application of multiobjective optimization (MOO) in machine learning (ML). The interest is driven by the numerous situations in real-life applications where multiple objectives need to be optimized simultaneously. A key aspect of MOO is the existence of a Pareto set, rather than a single optimal solution, which illustrates the inherent trade-offs between objectives. Despite its potential, there is a noticeable lack of satisfactory literature that could serve as an entry-level guide for ML practitioners who want to use MOO. Hence, our goal in this paper is to produce such a resource. We critically review previous studies, particularly those involving MOO in deep learning (using Physics-Informed Neural Networks (PINNs) as a guiding example), and identify misconceptions that highlight the need for a better grasp of MOO principles in ML. Using MOO of PINNs as a case study, we demonstrate the interplay between the data loss and the physics loss terms. We highlight the most common pitfalls one should avoid while using MOO techniques in ML. We begin by establishing the groundwork for MOO, focusing on well-known approaches such as the weighted sum (WS) method, alongside more complex techniques like the multiobjective gradient descent algorithm (MGDA). Additionally, we compare the results obtained from the WS and MGDA with one of the most common evolutionary algorithms, NSGA-II. We emphasize the importance of understanding the specific problem, the objective space, and the selected MOO method, while also noting that neglecting factors such as convergence can result in inaccurate outcomes and, consequently, a non-optimal solution. Our goal is to offer a clear and practical guide for ML practitioners to effectively apply MOO, particularly in the context of DL.