On the Impossibility of Global Convergence in Multi-Loss Optimization

Authors: Alistair Letcher

ICLR 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We negatively resolve this open problem by proving that desirable convergence properties cannot simultaneously hold for any algorithm. Our result has more to do with the existence of games with no satisfactory outcomes, than with algorithms per se. More explicitly we construct a two-player game with zero-sum interactions whose losses are both coercive and analytic, but whose only simultaneous critical point is a strict maximum.
Researcher Affiliation Academia The paper lists the author as 'Alistair Letcher aletcher.github.io'. No specific institutional affiliation (university or company name) is explicitly provided in the paper's header or body, preventing a definitive classification.
Pseudocode No The paper describes algorithms mathematically in Appendix A but does not provide structured pseudocode or algorithm blocks.
Open Source Code Yes Accompanying code for all experiments can be found at https://github.com/aletcher/ impossibility-global-convergence.
Open Datasets No The paper uses mathematically constructed 'games' (M and N) for its theoretical proofs and simulations, rather than publicly available datasets.
Dataset Splits No The paper does not specify training/validation/test dataset splits, as its focus is on theoretical proofs and simulations of constructed games.
Hardware Specification No The paper does not provide specific hardware details (e.g., GPU/CPU models, processor types) used for running its simulations.
Software Dependencies No The paper mentions 'Singular' for a mathematical proof but does not provide specific version numbers for any key software components or libraries used for the general experimental setup.
Experiment Setup Yes In all experiments we initialise θ0 following a standard normal distribution and use a learning rate α = 0.01, with γ = 0.01 for CO.