We demonstrate a multi-fidelity (MF) machine learning ensemble framework for the inverse design of photonic surfaces, trained on a dataset of 11,759 samples that we fabricate using high throughput femtosecond laser processing. The MF ensemble combines an initial low fidelity model for generating design solutions, with a high fidelity model that refines these solutions through local optimization. The combined MF ensemble can generate multiple disparate sets of laser-processing parameters that can each produce the same target input spectral emissivity with high accuracy (root mean squared errors < 2%). SHapley Additive exPlanations analysis shows transparent model interpretability of the complex relationship between laser parameters and spectral emissivity. Finally, the MF ensemble is experimentally validated by fabricating and evaluating photonic surface designs that it generates for improved efficiency energy harvesting devices. Our approach provides a powerful tool for advancing the inverse design of photonic surfaces in energy harvesting applications.

We consider a problem of placing generators of rewards to be collected by randomly moving agents in a network. In many settings, the precise mobility pattern may be one of several possible, based on parameters outside our control, such as weather conditions. The placement should be robust to this uncertainty, to gain a competent total reward across possible networks. To study such scenarios, we introduce the Robust Reward Placement problem (RRP). Agents move randomly by a Markovian Mobility Model with a predetermined set of locations whose connectivity is chosen adversarially from a known set $\Pi$ of candidates. We aim to select a set of reward states within a budget that maximizes the minimum ratio, among all candidates in $\Pi$, of the collected total reward over the optimal collectable reward under the same candidate. We prove that RRP is NP-hard and inapproximable, and develop $\Psi$-Saturate, a pseudo-polynomial time algorithm that achieves an $\epsilon$-additive approximation by exceeding the budget constraint by a factor that scales as $O(\ln |\Pi|/\epsilon)$. In addition, we present several heuristics, most prominently one inspired by a dynamic programming algorithm for the max-min 0-1 KNAPSACK problem. We corroborate our theoretical analysis with an experimental evaluation on synthetic and real data.

We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically affected by the rank and precision of the coupling matrices. By developing and assessing advanced decomposition techniques, we expand the range of problems SPIMs can solve, overcoming the limitations of traditional Mattis-type matrices. Our approach accommodates a diverse array of coupling matrices, including those with inherently low ranks, applicable to complex NP-complete problems. We explore the practical benefits of low-rank approximation in optimization tasks, particularly in financial optimization, to demonstrate the real-world applications of SPIMs. Finally, we evaluate the computational limitations imposed by SPIM hardware precision and suggest strategies to optimize the performance of these systems within these constraints.

The signed distance field is a popular implicit shape representation in robotics, providing geometric information about objects and obstacles in a form that can easily be combined with control, optimization and learning techniques. Most often, SDFs are used to represent distances in task space, which corresponds to the familiar notion of distances that we perceive in our 3D world. However, SDFs can mathematically be used in other spaces, including robot configuration spaces. For a robot manipulator, this configuration space typically corresponds to the joint angles for each articulation of the robot. While it is customary in robot planning to express which portions of the configuration space are free from collision with obstacles, it is less common to think of this information as a distance field in the configuration space. In this paper, we demonstrate the potential of considering SDFs in the robot configuration space for optimization, which we call the configuration space distance field. Similarly to the use of SDF in task space, CDF provides an efficient joint angle distance query and direct access to the derivatives. Most approaches split the overall computation with one part in task space followed by one part in configuration space. Instead, CDF allows the implicit structure to be leveraged by control, optimization, and learning problems in a unified manner. In particular, we propose an efficient algorithm to compute and fuse CDFs that can be generalized to arbitrary scenes. A corresponding neural CDF representation using multilayer perceptrons is also presented to obtain a compact and continuous representation while improving computation efficiency. We demonstrate the effectiveness of CDF with planar obstacle avoidance examples and with a 7-axis Franka robot in inverse kinematics and manipulation planning tasks.

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression does not always perform well due to the lack of flexibility. This paper enhances kernel ridgeless regression with Locally-Adaptive-Bandwidths (LAB) RBF kernels, incorporating kernel learning techniques to improve performance in both experiments and theory. For the first time, we demonstrate that functions learned from LAB RBF kernels belong to an integral space of Reproducible Kernel Hilbert Spaces (RKHSs). Despite the absence of explicit regularization in the proposed model, its optimization is equivalent to solving an $\ell_0$-regularized problem in the integral space of RKHSs, elucidating the origin of its generalization ability. Taking an approximation analysis viewpoint, we introduce an $l_q$-norm analysis technique (with $0

Reward learning involves inferring and shaping the underlying reward function from observed human demonstrations and feedback. Inverse reinforcement learning (IRL) and reinforcement learning from human feedback (RLHF, also known as preference-based reinforcement learning) are key methodologies in reward learning, applied in various sequential decision-making tasks such as games [1-3], robotics [4-6], and language models [7-11]. Particularly in the recent drastic development of large language models (LLMs), RLHF has played a crucial role in fine-tuning models to better align with human preferences [10]. However, despite the notable empirical success of these algorithms, a significant gap remains in the theoretical analysis of IRL and RLHF, limiting us to guarantee their reliability. This work aims to bridge this gap by proposing a novel theoretical framework for offline IRL and RLHF. IRL aims to infer a reward function that aligns with an expert behavior from demonstrations [12, 13]. Typical IRL algorithms employ a bi-level optimization framework within the context of maximum likelihood estimation (MLE). In this framework, the inner optimization evaluates the policy based on the current reward parameters, while the outer optimization updates these parameters to better match observed expert behavior. These algorithms have been extensively explored in the literature [14-18], and their convergence is studied in both online settings [17] and offline settings [18].

In recent years, significant attention has been directed towards learning average-reward Markov Decision Processes (MDPs). However, existing algorithms either suffer from sub-optimal regret guarantees or computational inefficiencies. In this paper, we present the first tractable algorithm with minimax optimal regret of $\widetilde{\mathrm{O}}(\sqrt{\mathrm{sp}(h^*) S A T})$, where $\mathrm{sp}(h^*)$ is the span of the optimal bias function $h^*$, $S \times A$ is the size of the state-action space and $T$ the number of learning steps. Remarkably, our algorithm does not require prior information on $\mathrm{sp}(h^*)$. Our algorithm relies on a novel subroutine, Projected Mitigated Extended Value Iteration (PMEVI), to compute bias-constrained optimal policies efficiently. This subroutine can be applied to various previous algorithms to improve regret bounds.

In various applications, the optimal policy in a strategic decision-making problem depends both on the environmental configuration and exogenous events. For these settings, we introduce Bilevel Optimization with Contextual Markov Decision Processes (BO-CMDP), a stochastic bilevel decision-making model, where the lower level consists of solving a contextual Markov Decision Process (CMDP). BO-CMDP can be viewed as a Stackelberg Game where the leader and a random context beyond the leader's control together decide the setup of (many) MDPs that (potentially multiple) followers best respond to. This framework extends beyond traditional bilevel optimization and finds relevance in diverse fields such as model design for MDPs, tax design, reward shaping and dynamic mechanism design. We propose a stochastic Hyper Policy Gradient Descent (HPGD) algorithm to solve BO-CMDP, and demonstrate its convergence. Notably, HPGD only utilizes observations of the followers' trajectories. Therefore, it allows followers to use any training procedure and the leader to be agnostic of the specific algorithm used, which aligns with various real-world scenarios. We further consider the setting when the leader can influence the training of followers and propose an accelerated algorithm. We empirically demonstrate the performance of our algorithm.

Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotics tasks. Due to the combinatorial complexity, the solving speed of hybrid MPC can be insufficient for real-time applications. In this paper, we propose to accelerate hybrid MPC using Generalized Benders Decomposition (GBD). GBD enumerates cuts online and stores inside a finite buffer to provide warm-starts for the new problem instances. Leveraging on the sparsity of feasibility cuts, a fast algorithm is designed for Benders master problems. We also propose to construct initial optimality cuts from heuristic solutions allowing GBD to plan for longer time horizons. The proposed algorithm successfully controls a cart-pole system with randomly moving soft-contact walls reaching speeds 2-3 times faster than Gurobi, oftentimes exceeding 1000Hz. It also guides a free-flying robot through a maze with a time horizon of 50 re-planning at 20Hz. The code is available at https://github.com/XuanLin/Benders-MPC.

We establish a new model-agnostic optimization framework for out-of-distribution generalization via multicalibration, a criterion that ensures a predictor is calibrated across a family of overlapping groups. Multicalibration is shown to be associated with robustness of statistical inference under covariate shift. We further establish a link between multicalibration and robustness for prediction tasks both under and beyond covariate shift. We accomplish this by extending multicalibration to incorporate grouping functions that consider covariates and labels jointly. This leads to an equivalence of the extended multicalibration and invariance, an objective for robust learning in existence of concept shift. We show a linear structure of the grouping function class spanned by density ratios, resulting in a unifying framework for robust learning by designing specific grouping functions. We propose MC-Pseudolabel, a post-processing algorithm to achieve both extended multicalibration and out-of-distribution generalization. The algorithm, with lightweight hyperparameters and optimization through a series of supervised regression steps, achieves superior performance on real-world datasets with distribution shift.