Prox-DASA-(GT): Decentralized Proximal Averaged Stochastic Approximation

---

In this file we provide instructions on experimental results of "A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization". We used the implementation of SPPDM, ProxGT-SR and DEEPSTORMv2 in https://github.com/gmancino/DEEPSTORM, and based on their framework we implemented Prox-DASA and Prox-DASA-GT.

Experiment set-up

All experiments were conducted on a laptop with Intel Core i7-11370H Processor and Windows 11 operating system. All code is written in Python version 3.9.15, using PyTorch version 1.13.1. and mpi4py version 3.1.4. See here for instructions on how to install this package.

A complete list of packages necessary for completing the experiments is located in the requirements.txt file.

Running experiments

For sake of example, we will use proxdasa.py as our test method here; see the methods folder for the other methods utilized in the experiments

1. Move desired method out of methods folder

For sake of organization, the actual methods utilized in the experiments are delegated to the methods folder. Move them into the root directory

2. Run experiments using the parameters listed below

Dataset	Parameters
a9a	--data='a9a' --updates=10001 --report=100 --l1=1e-4
MNIST	--data='mnist' --updates=3001 --report=100 --l1=1e-4

For a full list of required parameters specific to each method, refer to the following table:

Method	Dataset	Parameters
deepstormv2.py	a9a	--init_batch=1 --mini_batch=4 --comm_pattern='ring' --step_type='diminishing' --k0=5 --beta=0.031 --lr=10.0
	MNIST	--init_batch=1 --mini_batch=32 --comm_pattern='random' --step_type='diminishing' --k0=3 --beta=0.0228 --lr=5.0
proxgtsr.py	a9a	--mini_batch=4 --full_grad=1000 --comm_pattern='ring' --lr=5e-3
	MNIST	--mini_batch=32 --full_grad=32 --comm_pattern='random' --lr=0.1
sppdm.py	a9a	--mini_batch=4 --comm_pattern='ring' --c=1.0 --kappa=0.1 --gamma=3 --beta=0.9 --mom='nesterov' --alpha=0.01
	MNIST	--mini_batch=32 --comm_pattern='random' --c=1.0 --kappa=0.1 --gamma=3 --beta=0.9 --mom='nesterov' --alpha=0.1
proxdasa.py	a9a	--mini_batch=4 --comm_pattern='ring' --step_type='diminishing' --alpha_base=0.3 --lr=10.0
	MNIST	--mini_batch=32 --comm_pattern='random' --step_type='diminishing' --alpha_base=3.0 --lr=1.0
proxdasagt.py	a9a	--mini_batch=4 --comm_pattern='ring' --step_type='diminishing' --alpha_base=0.3 --lr=10.0
	MNIST	--mini_batch=32 --comm_pattern='random' --step_type='diminishing' --alpha_base=3.0 --lr=5.0

So a full example for running proxdasa.py on the a9a dataset over the ring communication graph is given by:

mpiexec -np 8 python proxdasa.py --data=a9a --updates=10001 --report=100 --l1=1e-4 --comm_pattern=ring --mini_batch=4 --lr=10

1. Reproduce the results from the paper by varying over all initializations

Append --trial=i for i=1,2,...,10 to the above code to record outputs across different initializations.

4. The results will be saved in the results folder

Summary

We have the following directories and files:

helpers/
init_weights/
mixing_matrices/
methods/
models/
results/
requirements.txt

data

The data folder contains subfolders housing the training/testing data used in the experiments. To add a new dataset, include the folders here and modify lines containing torch.utils.data.DataLoader in the corresponding methods file

helpers

The helpers folder contains helper functions utilized by all methods. These are:

1. replace_weights.py: a custom PyTorch optimizer that simply replaces model parameters from a LIST of PyTorch tensors; since all methods update many different variables, this is a straightforward way to minimize conflicts when updating model parameters. The .step() method requires two parameters:

   • weights: a LIST of PyTorch tensors of length k where k represents the number of model parameters
   • device: the torch device (i.e. GPU) the model is saved on

2. l1_regularizer.py: performs soft-thresholding of the weights in a LIST of PyTorch tensors via the .forward() method. Additionally, with the .number_non_zeros() method, we count the number of non-zero elements (up to error tolerance 1e-6) in a LIST of PyTorch tensors

3. custom_data_loader.py: loads the a9a dataset from their tensor files in the proper format

mixing_matrices

The mixing_matrices folder contains Numpy arrays of size N x N where each (i,j) entry corresponds to agent i's weighting of agent j's information

To run experiments with different weight matrices/communication patterns or sizes, save the corresponding mixing matrix in this directory

init_weights

The init_weights directory contains the initial parameters for each agent, for each random seed, used in the experiments. These are only uploaded for sake of completeness; to remove the need to save initial weights for future experiments, comment lines containing

[torch.tensor(init_weights[i]).to(self.device) for i in range(len(init_weights))]

and replace with

[p.data.detach().clone() for p in self.model.parameters()]

models

The models folder contains the neural network architectures used in the experiments

methods

The methods folder contains all of the different decentralized optimization methods compared in this work; see the paper for a list of those compared here

Citation

Please cite the following papers if you use this code in your work:

@inproceedings{mancino2023proximal,
  title={Proximal Stochastic Recursive Momentum Methods for Nonconvex Composite Decentralized Optimization},
  author={Mancino-ball, Gabriel and Miao, Shengnan and Xu, Yangyang and Chen, Jie},
  booktitle={AAAI Conference on Artificial Intelligence},
  publisher={{AAAI} Press},
  year={2023}
}

@inproceedings{xiao2023one,
  title={A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization},
  author={Xiao, Tesi and Chen, Xuxing and Balasubramanian, Krishnakumar and Ghadimi, Saeed},
  booktitle={Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
  publisher = {PMLR},
  year={2023}  
}