Reinforcement Learning in Nonzero-sum Linear Quadratic Deep Structured\n Games: Global Convergence of Policy Optimization
Bibliographic record
Abstract
We study model-based and model-free policy optimization in a class of\nnonzero-sum stochastic dynamic games called linear quadratic (LQ) deep\nstructured games. In such games, players interact with each other through a set\nof weighted averages (linear regressions) of the states and actions. In this\npaper, we focus our attention to homogeneous weights; however, for the special\ncase of infinite population, the obtained results extend to asymptotically\nvanishing weights wherein the players learn the sequential weighted mean-field\nequilibrium. Despite the non-convexity of the optimization in policy space and\nthe fact that policy optimization does not generally converge in game setting,\nwe prove that the proposed model-based and model-free policy gradient descent\nand natural policy gradient descent algorithms globally converge to the\nsub-game perfect Nash equilibrium. To the best of our knowledge, this is the\nfirst result that provides a global convergence proof of policy optimization in\na nonzero-sum LQ game. One of the salient features of the proposed algorithms\nis that their parameter space is independent of the number of players, and when\nthe dimension of state space is significantly larger than that of the action\nspace, they provide a more efficient way of computation compared to those\nalgorithms that plan and learn in the action space. Finally, some simulations\nare provided to numerically verify the obtained theoretical results.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".