heavyball 0.9.0

Efficient optimizers

HeavyBall

A simple package of efficient optimizers

The goal is not to thrive for completeness, full maintenance or abstraction, but instead to provide a simple largely static alternative to torch.optim with more and better optimizers.

Currently (2024-11-08, 0.7.4), the recommended optimizer is PrecondSchedulePaLMForeachSOAP.

Features

• Stochastic Rounding: FP32 convergence with BF16 parameters
• Inplace EMA: Same math, but less memory, less compute and higher stability
• Foreach: Fast multi-tensor application
• PaLM Beta2: Fast initial convergence, stable late convergence
• ScheduleFree: No learning rate schedule, but better convergence
• Preconditioner Schedule: Improved loss-per-step in early convergence, better step-per-second in late convergence (explained below)

Getting started

pip install heavyball

import torch
import heavyball

# Create a model
model = torch.nn.Linear(16, 1)

# Create an optimizer
optimizer = heavyball.PrecondSchedulePaLMForeachSOAP(model.parameters(), lr=1e-3)

x = torch.randn(128, 16)
y = torch.randn(128, 1)

for _ in range(1000):
    optimizer.zero_grad()
    loss = torch.nn.functional.mse_loss(model(x), y)
    loss.backward()
    optimizer.step()

Optimizers

Name	Description	Advantages / Disadvantages
ForeachAdamW	More efficient (speed, memory) AdamW	+ Faster than AdamW + Possibly more (numerically) stable
ForeachLaProp	More efficient (speed, memory) LaProp	+ Same cost as AdamW + Marginally better converence (better proofs) + Higher hyperparameter stability - Not a guaranteed win (can be neutral) - No "Slingshot"
ForeachADOPT	More efficient (speed, memory) ADOPT	+ Same cost as AdamW + Rigorous mathematical convergence proofs, even for challenging models (GANs) - Empirically underperforms LaProp - no bf16
ForeachSFAdamW	More efficient (speed, memory) ScheduleFree AdamW	+ Same cost as AdamW, but better eval perf + Full control over hyperparameters
PaLMForeachSFAdamW	ForeachSFAdamW with PaLM's beta2 schedule	+ Same cost as AdamW, but better eval perf + Less control, but faster early and more stable late convergence + ScheduleFree - slow early convergence
ForeachSOAP	More efficient (speed, memory) SOAP	+ Faster convergence (loss-at-step) + Full control over hyperparameters - more memory usage - more hyperparameters - higher overhead than AdamW (can be ammortized; better loss-at-second)
PaLMForeachSOAP	ForeachSOAP with PaLM's beta2 schedule	+ Faster convergence (loss-at-step) + Less control, but faster early and more stable late convergence - more memory usage - more hyperparameters - higher overhead than AdamW (can be ammortized; better loss-at-second)
SFPaLMForeachSOAP	ScheduleFree PaLMForeachSOAP	+ Fast convergence (loss-at-step) + less memory usage than PaLMForeachSOAP (more tham AdamW) - slower initial convergence than PaLMForeachSOAP (but allows higher LRs) - higher overhead than AdamW (can be ammortized)
PrecondScheduleSFPaLMForeachSOAP	SFPaLMForeachSOAP with preconditioner schedule, matching the error of PrecondEvery=2 with the cost of PrecondEvery=512	+ Better initial convergence than SFPaLMForeachSOAP + Significantly faster (sec/it) later + less memory usage than PaLMForeachSOAP (more tham AdamW) - slower initial convergence than PaLMForeachSOAP (but allows higher LRs) - higher overhead than AdamW (can be ammortized), goes to 0 with increasing number of step
PrecondSchedulePaLMForeachSOAP	PrecondScheduleSFPaLMForeachSOAP without schedule-free	+ Best initial convergence + Significantly faster (sec/it) later + high stability - more memory usage than PrecondScheduleSFPaLMForeachSOAP - higher overhead than AdamW (can be ammortized), goes to 0 with increasing number of steps
PrecondScheduleForeachSOAP	PrecondScheduleSFPaLMForeachSOAP without PaLM's beta2 schedule	+ Better initial convergence + Significantly faster (sec/it) later - more memory usage than PrecondScheduleSFPaLMForeachSOAP - higher overhead than AdamW (can be ammortized), goes to 0 with increasing number of steps

Precond Schedule

The default preconditioner schedule (f) would yield the following update intervals:

Steps	Interval, f	Total (schedule)	Total (constant, every 2)	Total (constant, every 16)
10	1.00005	10	5 (0.5x)	0 (0.0x)
100	1.026	99	50 (0.5x)	6 (0.1x)
1,000	2.0	738	500 (0.7x)	62 (0.1x)
10,000	14.3	2,168	5,000 (2.3x)	625 (0.3x)
100,000	100.2	4,049	50,000 (12.3x)	6,250 (1.5x)
1,000,000	513	7,245	500,000 (69.0x)	62,500 (8.6x)