Learning-Rate-Free Learning by D-Adaptation

Aaron Defazio ยท Konstantin Mishchenko

**Concept Graph & Resume using Claude 3.5 Sonnet | Chat GPT4o | Llama 3:**

graph LR
classDef adaptation fill:#d4f9d4, font-weight:bold, font-size:14px
classDef optimization fill:#f9d4d4, font-weight:bold, font-size:14px
classDef application fill:#d4d4f9, font-weight:bold, font-size:14px
classDef evaluation fill:#f9f9d4, font-weight:bold, font-size:14px
A[Learning-Rate-Free Learning by

D-Adaptation] --> B[D-Adaptation:

auto-setting

learning rates. 1] A --> C[Convex Lipschitz:

optimal convergence

rates. 2] A --> D[Subgradient

method:

minimizes convex

functions. 3] A --> E[Learning rate:

parameter controlling

updates. 4] A --> F[AdaGrad-Norm:

adaptive learning

rate method. 5] A --> G[Dual averaging:

optimization

framework. 6] B --> H[Lower bound:

maintains optimal

solution distance. 7] H --> I[Asymptotic

convergence:

optimal rate

at infinity. 8] I --> J[Non-asymptotic:

fixed iteration

performance. 9] I --> K[Coordinate-wise:

different rates

per dimension. 10] H --> L[Stochastic

optimization:

for noisy

gradients. 11] B --> M[SGD:

modified with

D-Adaptation. 12] M --> N[Adam:

integrates

D-Adaptation. 13] N --> O[Momentum:

accelerates

convergence. 14] O --> P[Learning rate

schedules:

predefined adjustment

patterns. 15] C --> Q[Convex

problems:

experimental

evaluations. 16] Q --> R[Image

classification:

training neural

networks. 17] R --> S[LSTM:

training

sequence models. 18] S --> T[Masked Language:

train BERT

models. 19] T --> U[Auto-regressive:

train GPT

models. 20] U --> V[Object Detection:

train identification

models. 21] A --> W[Vision Transformers:

train vision

tasks. 22] W --> X[fastMRI:

accelerating MRI

reconstruction. 23] X --> Y[Recommendation

Systems:

train personalized

models. 24] Y --> Z[Sensitivity

analysis:

performance

variations. 25] Z --> AA[Observed rates:

compared to

hand-tuned. 26] AA --> AB[Gradient Descent:

D-Adaptation

variant. 27] A --> AC[EMA:

technique in

Adam variant. 28] AC --> AD[Theoretical

guarantees:

convergence

proofs. 29] AD --> AE[Experimental

results:

evaluation across

tasks. 30] class B,C,D,E,F,G adaptation class H,I,J,K,L,M,N,O,P optimization class Q,R,S,T,U,V,W,X,Y,Z,AA,AB application class AC,AD,AE evaluation

D-Adaptation] --> B[D-Adaptation:

auto-setting

learning rates. 1] A --> C[Convex Lipschitz:

optimal convergence

rates. 2] A --> D[Subgradient

method:

minimizes convex

functions. 3] A --> E[Learning rate:

parameter controlling

updates. 4] A --> F[AdaGrad-Norm:

adaptive learning

rate method. 5] A --> G[Dual averaging:

optimization

framework. 6] B --> H[Lower bound:

maintains optimal

solution distance. 7] H --> I[Asymptotic

convergence:

optimal rate

at infinity. 8] I --> J[Non-asymptotic:

fixed iteration

performance. 9] I --> K[Coordinate-wise:

different rates

per dimension. 10] H --> L[Stochastic

optimization:

for noisy

gradients. 11] B --> M[SGD:

modified with

D-Adaptation. 12] M --> N[Adam:

integrates

D-Adaptation. 13] N --> O[Momentum:

accelerates

convergence. 14] O --> P[Learning rate

schedules:

predefined adjustment

patterns. 15] C --> Q[Convex

problems:

experimental

evaluations. 16] Q --> R[Image

classification:

training neural

networks. 17] R --> S[LSTM:

training

sequence models. 18] S --> T[Masked Language:

train BERT

models. 19] T --> U[Auto-regressive:

train GPT

models. 20] U --> V[Object Detection:

train identification

models. 21] A --> W[Vision Transformers:

train vision

tasks. 22] W --> X[fastMRI:

accelerating MRI

reconstruction. 23] X --> Y[Recommendation

Systems:

train personalized

models. 24] Y --> Z[Sensitivity

analysis:

performance

variations. 25] Z --> AA[Observed rates:

compared to

hand-tuned. 26] AA --> AB[Gradient Descent:

D-Adaptation

variant. 27] A --> AC[EMA:

technique in

Adam variant. 28] AC --> AD[Theoretical

guarantees:

convergence

proofs. 29] AD --> AE[Experimental

results:

evaluation across

tasks. 30] class B,C,D,E,F,G adaptation class H,I,J,K,L,M,N,O,P optimization class Q,R,S,T,U,V,W,X,Y,Z,AA,AB application class AC,AD,AE evaluation

**Resume: **

**1.-** D-Adaptation: A technique for automatically setting learning rates in optimization algorithms without requiring hyperparameter tuning.

**2.-** Convex Lipschitz functions: A class of mathematical functions for which D-Adaptation is proven to achieve optimal convergence rates.

**3.-** Subgradient method: An optimization algorithm that uses subgradients to minimize convex functions.

**4.-** Learning rate/step size: A parameter controlling how much an optimization algorithm updates parameters at each step.

**5.-** AdaGrad-Norm: An adaptive learning rate method that D-Adaptation builds upon.

**6.-** Dual averaging: An optimization framework that D-Adaptation uses as its foundation.

**7.-** Lower bound estimation: D-Adaptation maintains and updates a lower bound on the distance to the optimal solution.

**8.-** Asymptotic convergence: D-Adaptation achieves the optimal convergence rate as the number of iterations approaches infinity.

**9.-** Non-asymptotic analysis: Examination of D-Adaptation's performance for a fixed number of iterations.

**10.-** Coordinate-wise scaling: An extension of D-Adaptation to handle different learning rates for each parameter dimension.

**11.-** Stochastic optimization: Applying D-Adaptation to problems with noisy or sampled gradients.

**12.-** SGD with D-Adaptation: Modification of Stochastic Gradient Descent to incorporate D-Adaptation.

**13.-** Adam with D-Adaptation: Integration of D-Adaptation into the Adam optimizer.

**14.-** Momentum: A technique incorporated into D-Adaptation to accelerate convergence in certain scenarios.

**15.-** Learning rate schedules: Predefined patterns for adjusting learning rates, which can be combined with D-Adaptation.

**16.-** Convex problems: Experimental evaluation of D-Adaptation on various convex optimization tasks.

**17.-** Convolutional image classification: Application of D-Adaptation to training neural networks for image recognition.

**18.-** LSTM Recurrent Neural Networks: Using D-Adaptation for training sequence models in machine translation.

**19.-** Masked Language Modelling: Applying D-Adaptation to train BERT-like models for natural language processing.

**20.-** Auto-regressive Language Modelling: Using D-Adaptation to train GPT-like models for text generation.

**21.-** Object Detection: Applying D-Adaptation to train models for identifying objects in images.

**22.-** Vision Transformers: Using D-Adaptation to train transformer-based models for computer vision tasks.

**23.-** fastMRI: Application of D-Adaptation to train models for accelerating MRI image reconstruction.

**24.-** Recommendation Systems: Using D-Adaptation to train models for personalized content recommendations.

**25.-** Sensitivity analysis: Examining how D-Adaptation's performance varies with different initial parameter settings.

**26.-** Observed learning rates: Comparison of D-Adaptation's automatically chosen learning rates to hand-tuned values.

**27.-** Gradient Descent variant: A version of D-Adaptation applied to standard gradient descent optimization.

**28.-** Exponential Moving Average (EMA): A technique used in the Adam variant of D-Adaptation.

**29.-** Theoretical guarantees: Mathematical proofs of D-Adaptation's convergence properties and performance bounds.

**30.-** Experimental results: Comprehensive evaluation of D-Adaptation across various machine learning tasks and model architectures.

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