Derivative-Free Optimization

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6 papers in the last four weeks, with none the four weeks before. 0.1% of all new papers.

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Latest papers 16

Sep 30, 2026cs.AI

Code to Control: Synthesizing Parameterized Reactive Controllers

Recent LLM-based approaches to control either invoke a language model to select actions or synthesize world models that require planning at every decision, introducing latency that can limit real-time use. We introduce Code to Control, an approach that synthesizes Python controllers which execute directly as policies. Code to Control separates program structure from parameters. An LLM synthesizes the controller structure, while derivative-free search fits its parameters for continuous control using feedback from the environment. Once learned, the resulting controllers require neither LLM inference nor planning at decision time, enabling real-time gameplay and, under our timing protocol, faster action selection than a PPO policy. Across a suite of Atari games, Flappy Bird, and MuJoCo tasks, Code to Control outperforms planning-based program synthesis methods, remains competitive with deep reinforcement learning while using fewer environment interactions, transfers across substantial changes in environment dynamics, and scales to complex locomotion tasks.

Zergham Ahmed, Joshua B. Tenenbaum, Chris Bates +1

Harvard University · Massachusetts Institute of Technology · Florida Institute for Human and Machine Cognition

RL Control Language Model-Based Control LLM-Based Program Synthesis Derivative-Free Optimization

Sep 24, 2026cs.LG

SPADE-DFL: Communication-Efficient Decentralized Federated Learning via Derivative-Free Linearized ADMM

Reducing communication in derivative-free decentralized learning requires controlling the disagreement accumulated over multiple local updates. This paper develops SPADE-DFL, a primal--dual method that allows the number of local function-value updates between neighbor exchanges to grow with the computation budget while preserving the nonprivate convergence order. For smooth nonconvex objectives under uniform query-moment bounds, the prescribed nonprivate schedule achieves a time-averaged stationarity and consensus bound of

\mathcal{O}(T^{-1/3})

using only

Θ(T^{2/3})

communication rounds, where

T

is the number of local updates per client. For private training, the accumulated data-dependent increment is isolated from the graph correction, allowing one protected state per client and round to generate all outgoing messages. We prove client-level differential privacy for the full interactive transcript and quantify the resulting optimization error over a finite horizon. Experiments on four classification tasks show that SPADE-DFL achieves higher mean test accuracy than existing decentralized learning methods.

Mengli Wei, Mengkai Zhu, Jiawen Chen +2

School of Mathematics, Southeast University, Nanjing 210096, China

Communication-Efficient Distributed Training Black-Box Optimization Alternating Direction Method of Multipliers Decentralized Learning Differentially Private Federated Learning Derivative-Free Optimization+1

Sep 22, 2026cs.RO

Optimize, Learn, Refine: Whole-Body Grasping and Pick-and-Throw with a Spiral Soft Robot

Soft continuum robots can exploit distributed compliance for whole-body manipulation, but synthesizing behavior through changing contacts remains difficult. We address whole-body grasping and pick-and-throw from an initially ungrasped state through outcome-based actuation-space optimization. Grasping is quantified by tip angular sweep and body-object enclosure, while throwing further incorporates release-direction alignment and minimum release speed. These objectives allow grasping, acceleration, and release to emerge from compliant interaction without prescribing contact forces, contact locations, or body configurations. Because the resulting actuation-to-outcome mapping is nonsmooth, we utilize derivative-free CMA-ES within an optimize-learn-refine framework. CMA-ES generates solutions for sampled conditions, a task-conditioned predictor learns warm starts, and CMA-ES refines them for unseen conditions. In simulation, the method achieves 492/500 successful grasps (98.4%) and success rates of 98%, 97%, and 94% across three directional throwing trials. Learned initialization increases grasping success from 78.6% to 98.4% while reducing the median rollout count from 1184 to 816 in CMA-ES. Hardware experiments achieve a 100% grasping success rate across 50 executions and a 100% pick-and-throw success rate across 30 executions, with 10 repetitions per direction. Together, these simulation and hardware results demonstrate the effectiveness of the proposed framework across both simulated and physical whole-body manipulation tasks.

Marwah Basuhai, Tingcong Liu, Ibrahim Alsarraj +2

Robotic Grasping Whole-Body Robotic Manipulation Robotic Manipulation Dynamic Robotic Manipulation Continuum Robot Control Derivative-Free Optimization+1

Sep 15, 2026math.OC

Derivative-Free Structured Updates for Muon

Muon updates matrix-valued neural-network parameters by orthogonalizing a gradient-based momentum matrix. Its reliance on derivatives limits its use when gradients are unavailable or unreliable. We develop a derivative-free framework that constructs Muon-style updates from structured finite differences. Four variants are considered: full entrywise recovery, random low-rank surrogates, basis-aligned rank-one probing, and direct structured search. Exhaustive basis-aligned probing is equivalent, up to positive scaling before ideal polar orthogonalization, to coordinate finite differences. Matrix-regression experiments show that random rank-one probing can reduce the number of function evaluations substantially, at the cost of less accurate updates. Controlled noisy-gradient experiments on regression and a neural network illustrate when accurate function values can compensate for an unreliable gradient oracle. A small CartPole study further examines orthogonal rank-one probes under a fixed episode budget. These results support structured probing as a practical option for selected black-box problems; they do not establish a general convergence guarantee or an advantage over accurate, inexpensive gradients.

Pengcheng Xie

Lawrence Berkeley National Laboratory & University of California Berkeley, CA 94720, USA

Black-Box Optimization Zeroth-Order Optimization Neural Network Optimization Muon Optimizer Derivative-Free Optimization

Sep 14, 2026cs.RO

Trajectory Bundle Method in SE(3) for Black-Box Fixed-Wing Aircraft Trajectory Optimization

Dynamically feasible trajectory optimization for rigid-body systems is naturally formulated on the special Euclidean group SE(3) but is challenging when dynamics are available only as black-box computations without derivatives. This paper formulates the Trajectory Bundle Method (TBM) for motion planning implicitly on SE(3). Bundles are constructed in the Lie algebra and propagated through nonlinear rigid-body dynamics using exponential and logarithmic maps, enabling derivative-free planning of non-Euclidean trajectories. We show that Euclidean TBM interpolation error is bounded quadratically by bundle diameter and extend this result to SE(3), where the bound additionally depends on a local Lipschitz constant of the Log map. Numerical experiments corroborate these bounds. Finally, we demonstrate SE(3) TBM by optimizing an acrobatic, collision-free fixed-wing maneuver through a rotated aperture without explicit models or derivatives of the vehicle dynamics, aerodynamics, or collision model.

Matthew D. Osburn, Cameron K. Peterson, John L. Salmon

Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA · Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA

Trajectory Optimization Trajectory Generation Black-Box Optimization Lie Group Methods Motion Planning Derivative-Free Optimization

Sep 8, 2026cs.LG

Adaptively Incorporating Directional Hints into Zeroth-Order Optimization

We study zeroth-order optimization of non-convex functions with the aid of directional hints, which are cheap but potentially inaccurate approximations of the true gradient direction, given by linear subspaces at each iteration. To leverage these hints adaptively while maintaining robustness to their quality, we introduce Control-Variate Zeroth-Order Descent (CV-ZOD), a new framework that refines the classical zeroth-order gradient estimator with a control variate that can be set based on the directional hints. We first show that the oracle algorithm that optimally sets the reference vector and step size at each iteration achieves a convergence rate that interpolates between the first-order

O(1/T)

rate and the zeroth-order

O(d/T)

rate, depending on the quality of the hints along the trajectory. We then develop a practical variant of CV-ZOD that achieves the same oracle guarantee up to logarithmic factors, without any prior knowledge of the hint quality. We validate the method empirically on simulation-based scientific optimization tasks, demonstrating sustained progress on non-convex landscapes where zeroth-order descent is slower and existing guided methods stall as guidance deteriorates.

Alexander Ryabchenko, Jian Qian, Wenlong Mou

University of Toronto and Vector Institute · University of Hong Kong

Zeroth-Order Optimization Nonconvex Optimization Derivative-Free Optimization

Jul 1, 2026cs.LG

Generative Refinement for Low-Budget Black-Box Optimization

Black-box optimization is a fundamental tool in science and engineering for optimizing objectives when gradient information is unavailable. It becomes especially difficult when the objective function is expensive to evaluate, limiting the evaluation budget to a few tens or hundreds of queries, and when good solutions occupy complex, low-measure regions of the search space. Generative models can supply useful structural priors in such settings, but existing generative BBO approaches bring significant evaluation cost. We identify three design principles for generative optimization under such low-budget conditions: avoid objective learning, optimize in candidate space, and make every evaluation count. Together, these principles motivate separating structural modeling from objective-driven search. We instantiate them in SPARROW, a simple sequential optimizer that maintains a persistent, ranked archive of evaluated candidates and uses a fixed, unconditional generative sampler solely as a corruption-refinement operator. SPARROW requires only access to the sampler's corruption and refinement processes, and never needs to evaluate the objective to train or guide it. Across three complementary settings, probing thin feasible geometry, disconnected high-performing regions, and failure-prone evaluations, SPARROW outperforms classical and generative baselines under strict evaluation budgets. These results demonstrate that separating structural priors from objective-driven search can be effective when evaluations are scarce and the search geometry is challenging.

Edouard R. Dufour, Oliver Heinimann, Pascal Fua

CVLab EPFL Lausanne, CH

Black-Box Optimization Derivative-Free Optimization

Jun 24, 2026cs.LG

\chisao{}: A GPU-Native Parallel Optimizer for Multimodal Black-Box Functions via Convergence-Anticonvergence Oscillation

Finding all modes of a multimodal black-box function is a fundamental challenge in optimization, Bayesian inference, and scientific computing. Existing approaches -- basin-hopping, CMA-ES, multistart gradient descent -- operate sequentially and cannot exploit the massive parallelism of modern GPU hardware. We introduce \chisao{} (\textbf{C}onvergence-\textbf{H}alt-\textbf{I}nvert-\textbf{S}tick-\textbf{A}nd-\textbf{O}scillate), a GPU-native population optimizer that runs an entire sample batch simultaneously and exploits a deliberate convergence-anticonvergence oscillation cycle to escape local traps while freezing confirmed modes. The structural move is asymmetric: samples that reach true peaks are frozen (``stuck'') and preserved, while the rest keep exploring via momentum-based anti-convergence and stochastically smoothed gradients. Adaptive reseeding via two complementary strategies (Repulse Monkey and Golden Rooster) maintains population diversity throughout. On all 42 functions of the Simon Fraser University optimization benchmark suite across dimensions

d \in \{2, 4, 8, 16, 32, 64\}

, \chisao{} achieves \textbf{100%} mode recovery where all CPU baselines collapse at

d \geq 8

on the hardest multimodal functions, at up to \textbf{

34\times

} speedup over basin-hopping on functions where all methods succeed (Michalewicz

d=64

) and up to \textbf{

39\times

} on unimodal functions (Rotated Hyper-Ellipsoid

d=64

, pure GPU dividend). All benchmarks evaluate the objective by value alone -- gradients come from finite differences -- so the reported speedups are a derivative-free worst case. Under substantial likelihood noise (

σ_{\mathrm{noise}}

up to 1.0), mode detection remains 100% reliable. The algorithm is available as a standalone open-source Python package on PyPI.

Ira Wolfson

Department of Electronics and Electrical Engineering Braude College of Engineering, Karmiel, Israel

GPU Acceleration Black-Box Optimization High-Performance Computing Zeroth-Order Optimization Metaheuristic Optimization Global Optimization+2

May 29, 2026math.OC

Wall-Clock Complexity for Zeroth-Order Optimization with Tunable Oracle Fidelity

Zeroth-order (black-box) optimization is applied when gradients are unavailable and objective evaluations rely on expensive simulations. In many such applications, the oracle fidelity is tunable: higher-accuracy queries reduce noise but incur higher computational costs. To capture this trade-off, we study an accuracy-aware wall-clock model where each query with fidelity

δ

has a cost

c(δ)

, and we minimize the total time

T_{\mathrm{total}} = \sum_{k=1}^{N} c(δ_k)

, subject to a target accuracy constraint. We show how the choice of oracle type, noise model, and optimization scheme induces explicit wall-clock-optimal choices for the algorithmic parameters. For instance, we demonstrate that accelerated methods can be wall-clock inferior to non-accelerated schemes. Furthermore, we characterize the conditions under which a constant fidelity strategy is optimal in the Big-O sense. Our framework provides a unified methodology to translate convergence guarantees into practical fidelity and batching recommendations.

Alexandra Suvorikova, Igor Pavlov, Artem Vasin +4

Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany · Moscow Independent Research Institute of Artificial Intelligence, Moscow, Russia · MSU Institute for Artificial Intelligence, Moscow, Russia +3

Stochastic Optimization Oracle Complexity Zeroth-Order Optimization Derivative-Free Optimization

May 15, 2026cs.LG

Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing

Sampling-based optimization (SBO), like cross-entropy method and evolutionary algorithms, has achieved many successes in solving non-convex problems without gradients, yet its convergence is poorly understood. In this paper, we establish a non-asymptotic convergence analysis for SBO through the lens of smoothing. Specifically, we recast SBO as gradient descent on a smoothed objective, mirroring noise-conditioned score ascent in diffusion models. Our first contribution is a landscape analysis of the smoothed objective, demonstrating how smoothing helps escape local minima and uncovering a fundamental coverage-optimality trade-off: smoothing renders the landscape more benign by enlarging the locally convex region around the global minimizer, but at the cost of introducing an optimality gap. Building on this insight, we establish non-asymptotic convergence guarantees for SBO algorithms to a neighborhood of the global minimizer. Furthermore, we propose an annealed SBO algorithm, Diffusion-Inspired Dual-Annealing (DIDA), which is provably convergent to the global optimum. We conduct extensive numerical experiments to verify our landscape results and also demonstrate the compelling performance of DIDA compared to other gradient-free optimization methods. Lastly, we discuss implications of our results for diffusion models.

Zeji Yi, Chaoyi Pan, Guanya Shi +1

Carnegie Mellon University

Optimization Convergence Analysis Black-Box Optimization Global Optimization Nonconvex Optimization Stochastic Optimization Convergence Derivative-Free Optimization

May 15, 2026cs.LG

Position: Zeroth-Order Optimization in Deep Learning Is Underexplored, Not Underpowered

Zeroth-order (ZO) optimization, learning from finite differences of function evaluations without backpropagation, has recently regained attention in deep learning due to its memory efficiency and applicability to gray- or black-box pipelines. Yet, ZO methods are often dismissed as fundamentally unscalable because of estimator variance and unfavorable query complexity. We argue that this conclusion might be misguided: ZO optimization is underexplored, not underpowered. We show that many perceived limitations stem from myopic development practices, most notably full-space, element-wise, estimator-centric designs. We articulate six positions spanning the algorithmic, systems, and evaluation stack. First, we revisit the feasibility boundaries of estimator-centric ZO methods through variance control, variance-query tradeoffs, and directional-derivative lenses. Then, we identify three underexplored opportunities: (i) subspace and spectral views of ZO that enable interpretable variance reduction with graceful query scaling, (ii) the forward-only nature of ZO as a systems advantage for communication-efficient, pipeline-friendly, and resource-constrained training, and (iii) the need to de-obfuscate ZO evaluations from task complexity. We strongly advocate rethinking ZO optimization around its unique strengths and acting accordingly, opening a viable path toward large-scale, system-aware, and resource-efficient learning with ZO optimization.

Sijia Liu, Yicheng Lang, Soumyadeep Pal +6

1OPTML Lab, Michigan State University, USA · 2Lawrence Livermore National Laboratory, USA

Deep Learning Optimization Zeroth-Order Optimization Derivative-Free Optimization

May 12, 2026cs.LG

Gradient-Free Noise Optimization for Reward Alignment in Generative Models

Existing reward alignment methods for diffusion and flow models rely on multi-step stochastic trajectories, making them difficult to extend to deterministic generators. A natural alternative is noise-space optimization, but existing approaches require backpropagation through the generator and reward pipeline, limiting applicability to differentiable settings. To address this, here we present ZeNO (Zeroth-order Noise Optimization), a gradient-free framework that formulates noise optimization as a path-integral control problem, estimable from zeroth-order reward evaluations alone. When instantiated with an Ornstein--Uhlenbeck reference process, the update connects to Langevin dynamics implicitly targeting a reward-tilted distribution. ZeNO enables effective inference-time scaling and demonstrates strong performance across diverse generators and reward functions, including a protein structure generation task where backpropagation is infeasible.

Jeongsol Kim, Hongeun Kim, Jian Wang +1

KAIST AI1 · Snap Inc.2

Diffusion Model Alignment Stochastic Optimal Control Zeroth-Order Optimization Generative Modeling Derivative-Free Optimization

May 3, 2026cs.LG

Training Non-Differentiable Networks via Optimal Transport

Hard thresholds, quantization, and discrete routing can produce training losses with flat regions and jumps, where ordinary gradients vanish or are undefined. We introduce PolyStep, a forward-only optimizer that evaluates rotated polytope probes and moves parameter blocks along weighted averages of the probe directions. We derive the weights from one-sided entropic transport and use its uncoupled softmax solution in our primary experiments. Our analysis explains when variation among probe costs produces motion and when that motion decreases the loss. On a regular simplex, nonconstant costs always give a nonzero direction. For monotone ridge losses, the softmax update cannot increase the loss at any positive temperature; a perturbation bound gives sufficient conditions for descent near curved jumps. For bounded measurable losses, we randomize the probe radii and identify an exact smoothing whose gradient equals the expected linear cost-weighted direction up to scale. This identity yields a stationarity bound for an idealized fixed-temperature variant: under regularity and sampling assumptions stronger than those met by our trained configurations, the bound has an

O(T^{-1/2})

term and a persistent bias floor. We evaluate the practical method on networks with hard operations, discrete optimization, and policy search. On MNIST with hard-threshold spiking neurons, PolyStep reaches

93.0 \pm 0.2\%

, compared with

79.6 \pm 5.2\%

for the best-tuned gradient-free baseline at matched evaluations. These gains come with a query cost proportional to the search dimension per fresh step, which limits the number of updates available at a fixed budget.

An T. Le

Center for AI Research, VinUniversity, Vietnam · Intelligent Autonomous Systems, TU Darmstadt, Germany

Black-Box Optimization Neural Network Optimization Derivative-Free Optimization

Apr 23, 2026math.OC

BOOOM: Loss-Function-Agnostic Black-Box Optimization over Orthonormal Manifolds for Machine Learning and Statistical Inference

Optimization over the Stiefel manifold

\mathrm{St}(p,d)

, the set of

p \times d

column-orthonormal matrices, is fundamental in statistics, machine learning, and scientific computing, yet remains challenging in the presence of non-convex, non-smooth, or black-box objectives. Existing methods largely rely on either convex relaxations or gradient-based Riemannian optimization, limiting applicability in derivative-free and highly multimodal settings. We propose \textsc{BOOOM} (Black-box Optimization Over Orthonormal Manifolds), a general-purpose framework for loss-function-agnostic optimization on

\mathrm{St}(p,d)

. The key idea is a global Givens rotation-based parametrization that maps the manifold to an unconstrained Euclidean angle space while preserving feasibility exactly. Building on this representation, BOOOM employs a structured, parallelizable, derivative-free search based on Recursive Modified Pattern Search, enabling systematic exploration through plane-wise rotations without requiring gradient information and facilitating escape from poor local optima. We establish a unified theoretical framework showing equivalence between angle-space and manifold optimization, transfer of stationarity, and global convergence in probability under mild conditions. Empirical results across diverse problems, including heterogeneous quadratic optimization, low-rank and sparse matrix decomposition, independent component analysis, and orthogonal joint diagonalization, among other widely studied settings, demonstrate strong performance relative to state-of-the-art methods, particularly in non-smooth and highly multimodal regimes. We further illustrate its practical utility through a novel supervised PCA formulation applied to metabolomics data in colorectal cancer.

Beomchang Kim, Subhrajyoty Roy, Priyam Das

Department of Biostatistics, Virginia Commonwealth University, Richmond, VA, USA · Department of Statistics and Data Science, Washington University in St. Louis,[math.OC] St. Louis, MO, USA

Stiefel Manifold Optimization Black-Box Optimization Derivative-Free Optimization

Jan 31, 2026cs.NE

Meta-Learning-Assisted Constraint Relaxation for Constrained Black-Box Optimization

Constraint handling is central to constrained black-box optimization (BBO), where objective improvement and feasibility restoration often provide conflicting search signals. Existing

ε

-relaxation methods are simple and effective, but their relaxation schedules are usually fixed or manually designed for a limited range of problems. To address this limitation, this letter proposes MeCO, a meta-learning-assisted optimizer that learns an adaptive

ε

-relaxation policy for constrained BBO. MeCO couples a SHADE optimizer with a Double Deep Q-Network controller. At each optimization step, the controller observes compact population and constraint features and selects a scalar action, which is decoded into a relaxation vector for the candidate comparison rule. The policy is trained across constrained BBO instances and then deployed on held-out problems without problem-specific tuning. Experiments on the CEC2017 constrained benchmark, 16 UAV path-planning tasks and eight real-world engineering problems provide evidence that MeCO transfers across held-out benchmark functions, higher dimensions, and an application-domain setting. Ablation and behavior analyses further clarify the roles of constraint-related state features, action scaling, reward shaping, and meta-training.

Sijie Ma, Zeyuan Ma, Yue-Jiao Gong +1

Hong Kong Polytechnic University · South China Normal University · South China University of Technology

Black-Box Optimization Learning to Optimize Constrained Optimization Derivative-Free Optimization

Jun 30, 2025math.OC

Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies

Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we study CBO in the context of closed-box adversarial attacks, which are imperceptible input perturbations that aim to fool a classifier, without accessing its gradient. Our contribution is to establish a connection between the so-called consensus hopping as introduced by Riedl et al. and natural evolution strategies (NES) commonly applied in the context of adversarial attacks and to rigorously relate both methods to gradient-based optimization schemes. Beyond that, we provide a comprehensive experimental study that shows that despite the conceptual similarities, CBO can outperform NES and other evolutionary strategies in certain scenarios.

Tim Roith, Leon Bungert, Philipp Wacker

TUM School of Computation, Information and Technology and Munich Center for Machine Learning (MCML), Boltzmannstr. 3, 85748 Garching bei München, Germany · Institute of Mathematics, Center for Artificial Intelligence and Data Science (CAIDAS), University of Würzburg, Emil-Fischer-Str. 40, 97074 Würzburg, Germany · School of Mathematics and Statistics, University of Canterbury

Evolutionary Optimization Black-Box Adversarial Attacks Derivative-Free Optimization