Adaptive Learning Rate

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19 papers2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Oct 26, 2026

AHEAD: Adaptive Neural Acceleration for Large-Scale Linear Programming

Large-scale linear programs with millions of variables and constraints strain time and memory budgets. First-order methods such as the primal-dual hybrid gradient scale to this regime because they avoid matrix factorizations, but they require many iterations. Learned accelerators can reduce these iterations, yet fewer iterations do not guarantee a shorter solve. Learning inference also takes time, and running the accelerator longer trades solver time for inference time. Existing unrolled accelerators handle this trade-off poorly: each layer processes every variable and constraint, the predicted iterates still need solver refinement, and every instance runs the same layers. We therefore ask: What neural accelerator design achieves end-to-end speedups on large-scale linear programs across sizes and target accuracies? We introduce AHEAD, an accelerator that predicts step sizes for first-order linear programming solvers while keeping their update rules. Its weight-shared predictor reads compact solver statistics and rescales the primal and dual step sizes, so each warm-start iteration stays inexpensive and a short warm-start phase hands the solver a warm start. A learned handoff policy sets the number of warm-start iterations for each instance and target accuracy, after which the solver finishes under its own termination criterion. On packing linear programs with up to

10^7

variables, AHEAD achieves

6.5

--

11.6\times

end-to-end speedups over Gurobi's first-order solver from a cold start, including on instances of unseen sizes and distributions. The gains extend to PageRank linear programs and hold across difficulty levels and target accuracies.

Sihao Liu, Zhichao Hou, Huayue Gu +4

North Carolina State University · Kennesaw State University · Nokia Applied Research

Learning to Optimize Linear Programming Adaptive Learning Rate Primal-Dual Optimization

Oct 20, 2026

MuPACE: Learning to Pace Muon for LoRA Fine-Tuning

Learning rate schedules are typically fixed before training begins, yet when fine-tuning large language models with low-rank adapters (LoRA), the appropriate scale varies substantially with the model, task, and adapter configuration. Practitioners re-tune a schedule for every new problem, yet a tuned schedule still cannot react to the training dynamics it encounters. We instead amortize learning rate selection across LoRA fine-tuning problems. We leave the base optimizer, Muon, untouched, so that its normalized update fixes the direction, and meta-learn only the global step size. Our method MuPACE is a small recurrent policy, meta-trained across a distribution of fine-tuning runs, that conditions on the observed trajectory and emits bounded adjustments to an interpretable analytic schedule. On 64 fine-tuning problems, MuPACE outperforms standard fixed schedules at a strong shared default on 64-78% of problems and is on par with the same schedules with per-task tuned peaks. Meta-trained only on models with up to 16 layers, MuPACE transfers one-shot to unseen tasks on models as deep as 64 layers, such as Qwen3-32B and Qwen3.8-27B, where a single run remains competitive with swept schedules.

Jan Kobiolka, Christian Frey, Josif Grabocka

Department of Computer Science, University of Technology Nuremberg, Nuremberg, Germany

Learning Rate Scheduling Adaptive Learning Rate LLM Fine-Tuning Meta-Learning Parameter-Efficient Fine-Tuning

Sep 28, 2026

SOLAR: A State-Driven Online Learning Rate Scheduler for LLM Pretraining

Learning-rate (LR) scheduling plays a central role in large language model (LLM) pretraining, yet current practice still relies heavily on hand-crafted heuristics such as Warmup-Cosine-Decay and Warmup-Stable-Decay. Because these schedules are fixed in advance, they cannot adapt to evolving optimization dynamics. Online learned scheduling within the Learning to Optimize (L2O) framework offers a dynamic alternative, but remains brittle at LLM scale due to noisy signals, delayed feedback, and the risk of catastrophic divergence. We propose SOLAR (State-driven Online Learning rAte scheduleR), a stabilized framework for reliable online LR adaptation. SOLAR uses a base schedule as a reference and learns bounded, state-dependent residual corrections for individual parameter groups. Each correction re-anchors to the base at every step, allowing the policy to adapt the LR without relearning the warmup-decay profile. A lightweight state representation and progress-aware reward guide online learning, while a Circuit-Breaker restores training after rare unsafe actions. Across autoregressive language-model pretraining, SOLAR improves final perplexity over tuned static schedules and automatic LR tuners for dense models from 60M to 1B, AdamW and Muon, and two MoE settings up to 3B. Matched 130M controls show that adding base anchoring and action bounds improves a global PPO controller from 27.09 to 23.74 final PPL, while group-wise control reaches 22.87 on the same two seeds. A residual policy trained on a 60M proxy can also be frozen and reused at larger dense scales without target PPO updates, remaining effective across a fourfold base-LR range. These results establish SOLAR as a practical learned LR controller for LLM pretraining.

Qiulin Shang, Binyu Wang, Yongqi Qiao +3

Peking University · Nanjing University

Language Model Pretraining Learning Rate Scheduling Learning to Optimize Policy Learning Adaptive Learning Rate

Sep 5, 2026

One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning

Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models. Most LoRA variants follow a uniform-LR convention, applying a single global learning rate across every rank-one component of every adapter. We show that this convention overlooks substantial within-module heterogeneity, where the rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra that underutilize the nominal rank budget. To address this, we propose an adaptive anisotropic learning-rate model that assigns each rank-one component its own effective learning rate, computed online from training-time signals and mean-normalized per module to preserve the global LR budget. AnLR-LoRA instantiates this model with two signals available during AdamW optimization, namely function-space velocity and Adam SNR, as a lightweight scheme with no extra trainable parameters. Across commonsense reasoning, natural language generation and visual instruction-tuning benchmarks, AnLR-LoRA consistently improves over LoRA while encouraging broader use of rank capacity, with gains that remain robust across a wide range of global learning rates and transfer cleanly to other LoRA variants.

Huiyi Wang, Daijiao Liu, Lina Yao +1

University of New South Wales

LLM Fine-Tuning Low-Rank Adaptation Parameter-Efficient Fine-Tuning Adaptive Learning Rate

Jul 26, 2026

A Trust-region Framework for Moment Estimation

In this paper, we develop a trust-region framework for understanding the behavior of adaptive moment estimation mechanisms, such as Adam, in stochastic gradient optimization. Specifically, the magnitude of the update step associated with each individual parameter is constrained by a finite-order

p

-moment trust-region, with

p\ge1

. The resulting derivation leads to a family of learning-rate mechanisms based on second-moment estimation and normalized

p

-th-moment estimation. For

p=4

, this involves kurtosis estimation. Subsequent derivations provide a unified interpretation of moment-estimation-based normalization, learning-rate scheduling, momentum as a spectral first-order lowpass regularization, and operator-level spectral-norm normalization within a common trust-region framework. Preliminary experiments on GPT2-124M trained on FineWeb-Edu and TinyStories suggest that the fourth-moment realization provides its greatest benefit when trust-region constraints are weak. As progressively stronger trust-region controls are introduced, the second-moment realization becomes increasingly competitive, often achieving slightly lower validation loss than its corresponding fourth-moment realization.

Oluwasegun A. Somefun

Learning Rate Scheduling Trust-Region Optimization Adaptive Gradient Methods Adaptive Learning Rate

Jul 10, 2026

LionVote: Per-Layer Learning Rate Adaptation for Lion

Per-layer diagnostics reveal that, at the prescribed learning rate, Lion's effective scale is 2.6-2.8x too high for attention and MLP parameters and ~2x too high for normalization layers on ViT-Tiny/CIFAR-100; this 32% cross-layer-type disparity cannot be reproduced by a single global rate. The measurement comes from LionVote, a per-layer learning rate mechanism in which each parameter tensor maintains a compound level, a persistent integer updated every c epochs by two diagnostics (gradient direction stability and momentum health) resolved by a validation loss tiebreaker. Voting thresholds derive from geometric identities, the EMA time constant, and a noise-floor estimate; cadence is bounded structurally and selected by ablation. On ViT-Tiny/CIFAR-100, LionVote achieves 69.7% top-1 accuracy vs. Lion's 69.0% (p < 0.02, Welch's t-test) and AdamW's 68.8%. Per-layer adaptation value depends on both architectural heterogeneity and task; on uniform CNN architectures tuned SGD with cosine annealing remains dominant, and on ViT architectures gains are task-dependent.

Kris Atallah

New York University, New York, USA · New York University New York, NY, USA

Deep Learning Optimization Layer-Wise Learning Rate Adaptation Adaptive Learning Rate

Jul 6, 2026

ReCal3R: Reliability-Calibrated Learning Rates for Streaming 3D Reconstruction

Streaming 3D reconstruction relies on a compact recurrent scene state to process long image streams in linear time and bounded memory. However, repeated updates can gradually corrupt this state, causing reliable historical information to be overwritten by noisy or ambiguous observations. We introduce ReCal3R, a reliability-calibrated learning rate method for recurrent 3D reconstruction. Instead of directly applying a candidate learning rate, our method estimates state token reliability from the maintained scene state and uses it to calibrate a candidate learning rate derived from token alignment, state reconstruction residual, and recent update pressure. The resulting token-wise learning rate interpolates between a conservative base rate and the candidate rate, suppressing aggressive updates on unreliable tokens while preserving adaptation to informative frames. Applied to CUT3R as a training-free calibration rule, ReCal3R reaches strong performance on long sequences in pose, depth, and reconstruction quality, including a 3.7

\times

reduction in ATE, with comparable runtime and memory. Code is available at: https://github.com/Powertony102/ReCal3R.

Xinze Li, Yiyuan Wang, Pengxu Chen +4

Beijing Normal-Hong Kong Baptist University · Hong Kong Baptist University · Jilin University +2

Streaming 3D Reconstruction 3D Scene Representation Adaptive Learning Rate

Jun 20, 2026

Alternate loss functions and regression models that achieve robustness to outliers by modulating the learning rate

Most real-world datasets used for training supervised learning models are contaminated with noisy data and outliers leading to large prediction errors. This paper proposes a new approach for achieving robustness where the learning rate is modulated by a factor that is sensitive to outliers. In this approach a reduction of the learning rate is shown to be achieved by using alternate loss functions that are infinitely differentiable, strictly convex or quasiconvex and more closely approximate the absolute error than Huber and log-cosh losses. A comparison of the performance of regression models trained with different loss functions on a wide variety of benchmarks and datasets is presented to demonstrate the superior performance of the Square Root Loss (SRL) and Smooth Mean Absolute Error (SMAE) losses proposed in this paper. Two new robust linear regression models are presented. Highly vectorized robust parameter update formulae that take advantage of modern GPUs for both stochastic and batch gradient descent are presented.

Mathew Mithra Noel, Arindam Banerjee, Yug D. Oswal +2

aSchool of Electrical Engineering, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India · bErnst and Young GDS, Godrej Waterside, Ring Rd, DP Block, Sector V, Bidhannagar, Kolkata, 700 091, West Bengal, India · cSchool of Computer Science and Engineering, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India

Robust Regression Robust Loss Functions Adaptive Learning Rate Linear Regression Robust Estimation

Jun 4, 2026

Adaptive Learning Rates with Surrogate Probability for Follow-the-Perturbed-Leader

Follow-the-regularized-leader framework has shown effectiveness and flexibility in online learning problems, where the choice of learning rates are known to be crucial. Recently, adaptive learning rates defined in terms of the arm-selection probabilities, obtained by solving convex optimization, have achieved improved best-of-both-worlds (BOBW) guarantees in various bandit problems. In contrast, BOBW guarantees for its computationally efficient alternative, follow-the-perturbed-leader (FTPL), remain relatively limited since its optimization-free nature ironically makes the design of adaptive, probability-dependent learning rates non-trivial. To address this challenge, we propose an adaptive learning rate for FTPL by introducing surrogate probability functions that can be computed only from the available quantities, without requiring the exact probabilities. Based on these learning rates with surrogate functions, we provide the BOBW guarantee for FTPL with Pareto perturbations for any shape parameter

α>1

, generalizing prior results restricted to specific choices of

α=2

. We further show the BOBW guarantees for FTPL with adaptive learning rates in the bandit problem with expert advices. Our approach preserves the computational simplicity of FTPL while enabling probability-dependent adaptivity, and the surrogate-based methodology may be of independent interest in other algorithmic frameworks beyond FTPL and learning rate designs.

Jongyeong Lee, Junya Honda, Shinji Ito +1

Korea Institute of Science and Technology · Kyoto University · RIKEN AIP +2

Multi-Armed Bandits Follow-the-Perturbed-Leader Adaptive Learning Rate Adversarial Bandits

Jun 2, 2026

Physics-Guided Policy Optimization with Self-Distillation

Self-distilled policy optimization (SDPO) has become a popular paradigm for LLM post-training, where a model learns from its own predictions conditioned on privileged information. SDPO, however, is sensitive to how much each update step should be trusted: corrections from a self-teacher can be highly informative on some batches and misleading on others, and applying them uniformly with a fixed step size can destabilize training. Drawing inspiration from viscous-fluid dynamics and formalizing the analogy at the SDE level, we propose Physics-Guided Policy Optimization (PGPO), which introduces an information-modulated step-size multiplier derived from a mutual-information estimate between the student's predictions and the feedback-conditioned teacher. We show that this modulation preserves the order-1 weak-approximation guarantees of vanilla SGD, and incurs negligible overhead per iteration. We evaluate PGPO on the Science-QA dataset, where it outperforms SDPO on 3 of the 4 domains with gains of up to +4.5 points, while remaining stable in a setting where SDPO collapses late in training.

Ke Wang, Yuning Wu, Haoran Liu +3

Amazon, Arlington, USA · Amazon, New York, USA · Amazon, San Jose, USA +1

On-Policy Self-Distillation Policy Optimization Adaptive Learning Rate LLM Post-Training

Jun 1, 2026

Adaptive Sharpness-Aware Minimization with a Polyak-type Step size: A Theory-Grounded Scheduler

Sharpness-Aware Minimization (SAM) has established itself as a powerful and widely adopted optimizer for training machine learning models. By explicitly minimizing the sharpness of the loss landscape, SAM often improves generalization while delivering strong empirical performance. However, SAM and its variants, like most training algorithms, are sensitive to the choice of learning rate, which is typically selected through extensive hyperparameter tuning or predefined schedulers. In this work, motivated by recent advances on the effectiveness of stochastic Polyak step sizes for Stochastic Gradient Descent (SGD), we derive Polyak schedulers tailored to SAM-style updates, yielding novel adaptive algorithms in both deterministic and stochastic settings. In the smooth setting, we prove linear convergence for strongly convex objectives and an

\mathcal{O}(1/T)

convergence rate for convex objectives in the deterministic case. In the stochastic setting, we establish analogous convergence guarantees up to a neighborhood of the optimum. Numerical experiments demonstrate that the proposed Polyak schedulers achieve performance comparable to or better than carefully tuned SAM baselines, while substantially reducing the need for learning-rate tuning.

Dimitris Oikonomou, Nicolas Loizou

Mathematical Institute for Data Science (MINDS), Johns Hopkins University, Baltimore, MD, USA · Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA · Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA

Sharpness-Aware Minimization Learning Rate Scheduling Stochastic Optimization Convergence Adaptive Learning Rate

May 19, 2026

Fine-Tuning Without Forgetting via Loss-Adaptive Learning Rates

Fine-tuning large language models on new data improves task performance but degrades capabilities learned during pretraining, a phenomenon known as catastrophic forgetting. Existing methods mitigate this by modifying the fine-tuning objective to suppress high-loss tokens or sequences, but these tokens are essential for learning new tasks, especially those with poor pretraining coverage. In such settings, hard tokens should still contribute to learning, so forgetting must be controlled without suppressing them. We identify a simple mechanism for doing so: per-step forgetting is bounded by the product of the learning rate and the square root of the current training loss. This suggests that high-loss batches are especially prone to inducing forgetting. Motivated by this observation, we introduce FINCH, a loss-adaptive learning-rate schedule that reduces the learning rate on high-loss batches and increases it as the model converges, while leaving the fine-tuning objective unchanged. Across knowledge acquisition, science, and low-resource language adaptation benchmarks, FINCH reduces forgetting by 93% on average while matching the task performance of standard fine-tuning. On Qwen3-4B knowledge acquisition, FINCH cuts TruthfulQA degradation by 5x and reverses HaluEval degradation, while better preserving confidence calibration. Overall, our results show that learning-rate schedules are an effective tool to shape model behavior during fine-tuning, beyond just target-task optimization.

Parjanya Prajakta Prashant, Jiongli Zhu, Aldan Creo +1

University of California San Diego

Learning Rate Scheduling LLM Fine-Tuning Catastrophic Forgetting Adaptive Learning Rate

Apr 30, 2026

Learning Rate Engineering: From Coarse Single Parameter to Layered Evolution

Learning rate scheduling has evolved from the single global fixed rate of early SGD to sophisticated layer-wise adaptive strategies. We systematize this evolution into five generations: (Gen1) global fixed learning rates, (Gen2) global scheduling, (Gen3) parameter-level adaptation, (Gen4) layer-level differentiation, and (Gen5) joint layer-time scheduling. We trace the fundamental motivation behind each transition, showing how the shift from one-size-fits-all to tailoring by layer and time addresses the impossible trinity of transfer learning: lower layers require small updates to preserve general knowledge while higher layers need large updates to adapt to new tasks. Building on this taxonomy, we propose Discriminative Adaptive Layer Scaling (DALS), a unified framework that integrates phase-adaptive cosine scheduling, depth-aware Grokfast gradient filtering, and LARS-style trust ratios into a single coherent optimizer. We benchmark 18 strategies including three DALS variants across all five generations on five datasets: synthetic, CIFAR-10 (from scratch), RTE, TREC-6, and IMDb (fine-tuning). On synthetic, DALS achieves the best accuracy at 98.0%, while DALS-Fast reaches 90% in just 3 epochs. The cross-dataset analysis reveals striking regime-dependent patterns -- no single strategy wins across all regimes. Critically, STLR+Discriminative, the ULMFiT champion, catastrophically fails on from-scratch tasks (43.6% on TREC-6 from scratch vs. 96.8% with RAdam), confirming that directional decay biases are harmful without pretrained features. DALS avoids either extreme, achieving the best synthetic result while maintaining competitive fine-tuning performance.

Ming-Hong Yao, Di Wang, Jian Cui +5

School of AI, Jilin International Sciences University, Changchun, China.

Deep Learning Optimization Fine-Tuning Learning Rate Scheduling Adaptive Gradient Methods Layer-Wise Learning Rate Adaptation Adaptive Learning Rate

Mar 10, 2026

MetaDAT: Generalizable Trajectory Prediction via Meta Pre-training and Data-Adaptive Test-Time Updating

Existing trajectory prediction methods exhibit significant performance degradation under distribution shifts during test time. Although test-time training techniques have been explored to enable adaptation, current approaches rely on an offline pre-trained predictor that lacks online learning flexibility. Moreover, they depend on fixed online model updating rules that do not accommodate the specific characteristics of test data. To address these limitations, we first propose a meta-learning framework to directly optimize the predictor for fast and accurate online adaptation, which performs bi-level optimization on the performance of simulated test-time adaptation tasks during pre-training. Furthermore, at test time, we introduce a data-adaptive model updating mechanism that dynamically adjusts the predefined learning rates and updating frequencies based on online partial derivatives and hard sample selection. This mechanism enables the online learning rate to suit the test data, and focuses on informative hard samples to enhance efficiency. Experiments are conducted on various challenging cross-dataset distribution shift scenarios, including nuScenes, Lyft, and Waymo. Results demonstrate that our method achieves superior adaptation accuracy, surpassing state-of-the-art test-time training methods for trajectory prediction. Additionally, our method excels under suboptimal learning rates and high FPS demands, showcasing its robustness and practicality.

Yuning Wang, Pu Zhang, Yuan He +2

State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, IAIR, Xi’an Jiaotong University, China · KargoBot, China

Adaptive Learning Rate Trajectory Prediction Test-Time Adaptation Vehicle Trajectory Prediction Meta-Learning

Mar 1, 2026

Fed-ADE: Adaptive Learning Rate for Federated Post-adaptation under Distribution Shift

Federated learning (FL) in post-deployment settings must adapt to non-stationary data streams across heterogeneous clients without access to ground-truth labels. A major challenge is learning rate selection under client-specific, time-varying distribution shifts, where fixed learning rates often lead to underfitting or divergence. We propose Fed-ADE (Federated Adaptation with Distribution Shift Estimation), an unsupervised federated adaptation framework that leverages lightweight estimators of distribution dynamics. Specifically, Fed-ADE employs uncertainty dynamics estimation to capture changes in predictive uncertainty and representation dynamics estimation to detect covariate-level feature drift, combining them into a per-client, per-timestep adaptive learning rate. We provide theoretical analyses showing that our dynamics estimation approximates the underlying distribution shift and yields dynamic regret and convergence guarantees. Experiments on image and text benchmarks under diverse distribution shifts (label and covariate) demonstrate consistent improvements over strong baselines. These results highlight that distribution shift-aware adaptation enables effective and robust federated post-adaptation under real-world non-stationarity.

Heewon Park, Mugon Joe, Miru Kim +2

Department of Electrical and Computer Engineering, Sungkyunkwan University, Republic of Korea · Soongsil University, Seoul, Republic of Korea

Adaptive Learning Rate Federated Learning Distribution Shift Unsupervised Domain Adaptation

Oct 3, 2025

Why Do We Need Warm-up? A Theoretical Perspective

Learning rate warm-up -- increasing the learning rate at the beginning of training -- has become a ubiquitous heuristic in modern deep learning, yet its theoretical foundations remain poorly understood. In this work, we provide a principled explanation for why warm-up improves training. We rely on a generalization of the

(L_0, L_1)

-smoothness condition, which bounds local curvature as a linear function of the loss suboptimality and exhibits desirable closure properties. We show -- both theoretically and empirically -- that this condition is satisfied by common neural architectures and accurately captures the curvature of the optimization landscape early in training. Adapting the learning rate in response to this curvature condition naturally induces a warm-up-like schedule, and we show that this choice yields provably faster convergence guarantees than using a fixed learning rate. Experiments on language and vision models show that the resulting one-parameter warm-up schedule can match tuned linear warm-up and improve over no warm-up.

Foivos Alimisis, Rustem Islamov, Aurelien Lucchi

University of Basel, Switzerland

Deep Learning Optimization Learning Rate Scheduling Neural Network Training Dynamics Adaptive Learning Rate

Sep 22, 2025

Development of Deep Learning Optimizers: Approaches, Concepts, and Update Rules

Deep learning optimizers are optimization algorithms that enable deep neural networks to learn. The effectiveness of learning is highly dependent on the optimizer employed in the training process. Alongside the rapid advancement of deep learning, a wide range of optimizers with different approaches have been developed. This study aims to provide a review of various optimizers that have been proposed and received attention in the literature. From Stochastic gradient descent to the most recent ones such as Momentum, AdamW, Sophia, and Muon in chronological order, optimizers are examined individually, and their distinctive features are highlighted in the study. The update rule of each optimizer is presented in detail, with an explanation of the associated concepts and variables. The techniques applied by these optimizers, their contributions to the optimization process, and their default hyperparameter settings are also discussed. In addition, insights are offered into the open challenges encountered in the optimization of deep learning models. Thus, a comprehensive resource is provided both for understanding the current state of optimizers and for identifying potential areas of future development.

Doğay Altınel

Istanbul Medeniyet University

Deep Learning Optimization Neural Network Optimization Adaptive Gradient Methods Adaptive Learning Rate Stochastic Gradient Descent

Jun 20, 2024

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates). In practice, human-tuned deterministic learning rate schedules or small constant learning rates are often used, and implementations in machine learning frameworks like Tensorflow and Pytorch typically employ constant learning rates. We propose a learning-rate-adaptive approach for SGD methods, adjusting the learning rate based on empirical estimates for the objective function values. Specifically, we propose a learning-rate-adaptive variant of the Adam optimizer and implement it for several machine learning problems, including deep learning methods for partial differential equations such as deep Kolmogorov methods, physics-informed neural networks, and deep Ritz methods. We refer to https://github.com/deeplearningmethods/adaptive-learning-rate for the Python source codes for the numerical simulations in this work. Our results show that the proposed adaptive Adam variant achieves faster reductions of the objective function value compared to Adam with default learning rates. For certain quadratic minimization problems, we rigorously prove that an adaptive SGD variant converges to the global minimizer. This proof uses properties of invariant measures of the SGD dynamics and a generalized convergence analysis for SGD with random predictable learning rates which we develop in this work.

Steffen Dereich, Arnulf Jentzen, Adrian Riekert

Institute for Mathematical Stochastics, University of Münster, Germany · School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen), China · Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Germany

Adaptive Learning Rate Stochastic Optimization Convergence Adaptive Gradient Methods Stochastic Gradient Descent

Jun 1, 2023

Chaos persists in large-scale multi-agent learning despite adaptive learning rates

Multi-agent learning is intrinsically harder, more unstable and unpredictable than single agent optimization. For this reason, numerous specialized heuristics and techniques have been designed towards the goal of achieving convergence to equilibria in self-play. One such celebrated approach is the use of dynamically adaptive learning rates. Although such techniques are known to allow for improved convergence guarantees in small games, it has been much harder to analyze them in more relevant settings with large populations of agents. These settings are particularly hard as recent work has established that learning with fixed rates will become chaotic given large enough populations.In this work, we show that chaos persists in large population congestion games despite using adaptive learning rates even for the ubiquitous Multiplicative Weight Updates algorithm, even in the presence of only two strategies. At a technical level, due to the non-autonomous nature of the system, our approach goes beyond conventional period-three techniques Li-Yorke by studying fundamental properties of the dynamics including invariant sets, volume expansion and turbulent sets. We complement our theoretical insights with experiments showcasing that slight variations to system parameters lead to a wide variety of unpredictable behaviors.

Emmanouil-Vasileios Vlatakis-Gkaragkounis, Konstantinos Metaxas, Lampros Flokas +1

University of California, Berkeley. · Columbia University. · Singapore University of Technology and Design. +1

Adaptive Learning Rate Congestion Games Game-Theoretic RL