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Paper · 2302.03407 · ICML · 2023

Averaged Method of Multipliers for Bi-Level Optimization without Lower-Level Strong Convexity

Risheng Liu, Shangzhi Zeng, Jin Zhang, Wei Yao, Yaohua Liu

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 8 functions out of this paper's own repositories and ran 7 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
vis-opt-group/sl-bamm reimplementation 6 of 7
copy not recorded — 1 of 1
FunctionStatusWhere it lives
cat_list_to_tensor Ran this paper's copy was not recorded; identical code first harvested from junjieyang97/mrvrbo
pointer only · get_code("3ed1406329714c3f")
cg Ran vis-opt-group/sl-bamm/hypergrad/CG_torch.py
code served (permissive licence) · get_code("ccd4881b531f738e")
fixed_point Ran vis-opt-group/sl-bamm/hypergrad/hypergradients.py
code served (permissive licence) · get_code("cd2cd81580a4b699")
get_outer_gradients Ran vis-opt-group/sl-bamm/hypergrad/hypergradients.py
code served (permissive licence) · get_code("718723909e4de80c")
grad_unused_zero Ran vis-opt-group/sl-bamm/hypergrad/hypergradients.py
code served (permissive licence) · get_code("1b9c1e465ef0029f")
loss_L1 Ran vis-opt-group/sl-bamm/merely_convex/strategy3.py
code served (permissive licence) · get_code("452ac773b1804bc4")
loss_L2 Ran vis-opt-group/sl-bamm/merely_convex/strategy3.py
code served (permissive licence) · get_code("1592bf271df76b62")
update_tensor_grads Not yet run vis-opt-group/sl-bamm/hypergrad/hypergradients.py
code served (permissive licence) · get_code("43e10b662538de12")

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Abstract

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning fields. The validity of existing works heavily rely on either a restrictive Lower-Level Strong Convexity (LLSC) condition or on solving a series of approximation subproblems with high accuracy or both. In this work, by averaging the upper and lower level objectives, we propose a single loop Bi-level Averaged Method of Multipliers (sl-BAMM) for BLO that is simple yet efficient for large-scale BLO and gets rid of the limited LLSC restriction. We further provide non-asymptotic convergence analysis of sl-BAMM towards KKT stationary points, and the comparative advantage of our analysis lies in the absence of strong gradient boundedness assumption, which is always required by others. Thus our theory safely captures a wider variety of applications in deep learning, especially where the upper-level objective is quadratic w.r.t. the lower-level variable. Experimental results demonstrate the superiority of our method.

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