Evolutionary model merging enables the creation of high-performing multi-task models but remains computationally prohibitive for consumer hardware. We introduce MERGE$^3$, an efficient framework that makes evolutionary merging feasible on a single GPU by reducing fitness computation costs 50$\times$ while preserving performance. MERGE$^3$ achieves this by Extracting a reduced dataset for evaluation, Estimating model abilities using Item Response Theory (IRT), and Evolving optimal merges via IRT-based performance estimators. Our method enables state-of-the-art multilingual and cross-lingual merging, transferring knowledge across languages with significantly lower computational overhead. We provide theoretical guarantees and an open-source library, democratizing high-quality model merging.

Ground truth labels/outcomes are critical for advancing scientific and engineering applications, e.g., evaluating the treatment effect of an intervention or performance of a predictive model. Since randomly sampling inputs for labeling can be prohibitively expensive, we introduce an adaptive labeling framework where measurement effort can be reallocated in batches. We formulate this problem as a Markov decision process where posterior beliefs evolve over time as batches of labels are collected (state transition), and batches (actions) are chosen to minimize uncertainty at the end of data collection. We design a computational framework that is agnostic to different uncertainty quantification approaches including those based on deep learning, and allows a diverse array of policy gradient approaches by relying on continuous policy parameterizations. On real and synthetic datasets, we demonstrate even a one-step lookahead policy can substantially outperform common adaptive labeling heuristics, highlighting the virtue of planning. On the methodological side, we note that standard REINFORCE-style policy gradient estimators can suffer high variance since they rely only on zeroth order information. We propose a direct backpropagation-based approach, Smoothed-Autodiff, based on a carefully smoothed version of the original non-differentiable MDP. Our method enjoys low variance at the price of introducing bias, and we theoretically and empirically show that this trade-off can be favorable.

Heterogeneity poses a fundamental challenge for many real-world large-scale decision-making problems but remains largely understudied. In this paper, we study the fully heterogeneous setting of a prominent class of such problems, known as weakly-coupled Markov decision processes (WCMDPs). Each WCMDP consists of $N$ arms (or subproblems), which have distinct model parameters in the fully heterogeneous setting, leading to the curse of dimensionality when $N$ is large. We show that, under mild assumptions, a natural adaptation of the ID policy, although originally proposed for a homogeneous special case of WCMDPs, in fact achieves an $O(1/\sqrt{N})$ optimality gap in long-run average reward per arm for fully heterogeneous WCMDPs as $N$ becomes large. This is the first asymptotic optimality result for fully heterogeneous average-reward WCMDPs. Our techniques highlight the construction of a novel projection-based Lyapunov function, which witnesses the convergence of rewards and costs to an optimal region in the presence of heterogeneity.

In recent years, there has been much work on scaling Bayesian Optimization to high-dimensional problems, for example hyperparameter tuning in large neural network models. These scalable methods have been successful, finding high objective values much more quickly than traditional global Bayesian Optimization or random search-based methods. At the same time, these large neural network models often use sensitive data, but preservation of Differential Privacy has not scaled alongside these modern Bayesian Optimization procedures. Here we develop a method to privately estimate potentially high-dimensional parameter spaces using Gradient Informative Bayesian Optimization. Our theoretical results prove that under suitable conditions, our method converges exponentially fast to a ball around the optimal parameter configuration. Moreover, regardless of whether the assumptions are satisfied, we show that our algorithm maintains privacy and empirically demonstrates superior performance to existing methods in the high-dimensional hyperparameter setting.

Precise alignment in Text-to-Image (T2I) systems is crucial to ensure that generated visuals not only accurately encapsulate user intents but also conform to stringent ethical and aesthetic benchmarks. Incidents like the Google Gemini fiasco, where misaligned outputs triggered significant public backlash, underscore the critical need for robust alignment mechanisms. In contrast, Large Language Models (LLMs) have achieved notable success in alignment. Building on these advancements, researchers are eager to apply similar alignment techniques, such as Direct Preference Optimization (DPO), to T2I systems to enhance image generation fidelity and reliability. We present YinYangAlign, an advanced benchmarking framework that systematically quantifies the alignment fidelity of T2I systems, addressing six fundamental and inherently contradictory design objectives. Each pair represents fundamental tensions in image generation, such as balancing adherence to user prompts with creative modifications or maintaining diversity alongside visual coherence. YinYangAlign includes detailed axiom datasets featuring human prompts, aligned (chosen) responses, misaligned (rejected) AI-generated outputs, and explanations of the underlying contradictions.

Many machine learning methods look for low-dimensional representations of the data. The underlying subspace can be estimated by first choosing a dimension $q$ and then optimizing a certain objective function over the space of $q$-dimensional subspaces (the Grassmannian). Trying different $q$ yields in general non-nested subspaces, which raises an important issue of consistency between the data representations. In this paper, we propose a simple trick to enforce nestedness in subspace learning methods. It consists in lifting Grassmannian optimization problems to flag manifolds (the space of nested subspaces of increasing dimension) via nested projectors. We apply the flag trick to several classical machine learning methods and show that it successfully addresses the nestedness issue.

This paper introduces a new mission planning algorithm for autonomous robots that enables the reward-based selection of an optimal waypoint sequence from a predefined set. The algorithm computes a feasible trajectory and corresponding control inputs for a robot to navigate between waypoints while avoiding obstacles, maximizing the total reward, and adhering to constraints on state, input and its derivatives, mission time window, and maximum distance. This also solves a generalized prize-collecting traveling salesman problem. The proposed algorithm employs a new genetic algorithm that evolves solution candidates toward the optimal solution based on a fitness function and crossover. During fitness evaluation, a penalty method enforces constraints, and the differential flatness property with clothoid curves efficiently penalizes infeasible trajectories. The Euler spiral method showed promising results for trajectory parameterization compared to minimum snap and jerk polynomials. Due to the discrete exploration space, crossover is performed using a dynamic time-warping-based method and extended convex combination with projection. A mutation step enhances exploration. Results demonstrate the algorithm's ability to find the optimal waypoint sequence, fulfill constraints, avoid infeasible waypoints, and prioritize high-reward ones. Simulations and experiments with a ground vehicle, quadrotor, and quadruped are presented, complemented by benchmarking and a time-complexity analysis.

This paper presents a unified framework for codifying and automating optimization strategies to efficiently deploy deep neural networks (DNNs) on resource-constrained hardware, such as FPGAs, while maintaining high performance, accuracy, and resource efficiency. Deploying DNNs on such platforms involves addressing the significant challenge of balancing performance, resource usage (e.g., DSPs and LUTs), and inference accuracy, which often requires extensive manual effort and domain expertise. Our novel approach addresses two key issues: cross-stage co-optimization and optimization search. By seamlessly integrating programmatic DNN optimization techniques with high-level synthesis (HLS)-based metaprogramming and leveraging advanced design space exploration (DSE) strategies like Bayesian optimization, the framework automates both top-down and bottom-up design flows, reducing the need for manual intervention and domain expertise. The proposed framework introduces customizable optimization, transformation, and control blocks to enhance DNN accelerator performance and resource efficiency. Experimental results demonstrate up to a 92\% DSP and 89\% LUT usage reduction for select networks, while preserving accuracy, along with a 15.6-fold reduction in optimization time compared to grid search. These results underscore the novelty and potential of the proposed framework for automated, resource-efficient DNN accelerator designs.

Discriminative dictionary learning (DL) has been widely studied in various pattern classification problems. Most of the existing DL methods aim to learn a synthesis dictionary to represent the input signal while enforcing the representation coefficients and/or representation residual to be discriminative.

The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem [1, 2, 3, 4]. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over continuous space. Central to the method is a stochastic process recently described in mathematical statistics that we call the Gumbel process.