← 研踪 PaperTrailarXiv:2411.19193 · v4
The Price of Failure Risk: Clipped Barrier Policy Gradients with Convex Regularization
首次提交 2024-11-28 23:04
版本更新 2026-10-29 15:50
雷达观测 2026-10-30 13:28
摘要
In many control problems, actions consume a resource budget, such as a wear allowance, and the probability of exhausting it within a given horizon must stay below a tolerance. A simple, widely used approach is to augment the state with the remaining budget, subtract an interior barrier from the utility and penalize exhaustion, so that policy-gradient methods can be applied unchanged. We clip the combined one-step reward from below at a level m to keep the returns of exploratory policies finite. The clip level is a price of failure risk, since the clipped value decomposes exactly into the utility before failure, the cost of the interior margin and m times a geometric failure risk. Consequently, an approximately optimal policy maximizes utility net of margin cost among policies with no greater risk. Its risk exceeds that of any comparison policy by at most order 1/m and can be certified from its value or from validation data. Our main result proves exponential convergence of the population policy-gradient flow for every parameter regularizer that is convex along generalized geodesics and sufficiently strong relative to the price. This extends the mean-field analysis from relative entropy to weight decay and to finite networks. Relative entropy adds parameter noise and a pull toward a prior, whereas weight decay provides only the pull. Action regularization bounds changes in failure risk by the relative entropy to a reference policy. The bounds are evaluated on an exact maintenance benchmark, a fuel-tank controller, a solvable flow and a benchmark-suite task.
作者备注：40 pages, 8 figures, 1 table; Online Resource 1 (36 pages) as an ancillary file. Revised version; replaces v3 (text revised, the paper made independent of the Online Resource). Code: https://github.com/pma-papers/bpg-replication
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v4 · 2026-10-29 15:50 · 最新观测版本
The Price of Failure Risk: Clipped Barrier Policy Gradients with Convex Regularization
In many control problems, actions consume a resource budget, such as a wear allowance, and the probability of exhausting it within a given horizon must stay below a tolerance. A simple, widely used approach is to augment the state with the remaining budget, subtract an interior barrier from the utility and penalize exhaustion, so that policy-gradient methods can be applied unchanged. We clip the combined one-step reward from below at a level m to keep the returns of exploratory policies finite. The clip level is a price of failure risk, since the clipped value decomposes exactly into the utility before failure, the cost of the interior margin and m times a geometric failure risk. Consequently, an approximately optimal policy maximizes utility net of margin cost among policies with no greater risk. Its risk exceeds that of any comparison policy by at most order 1/m and can be certified from its value or from validation data. Our main result proves exponential convergence of the population policy-gradient flow for every parameter regularizer that is convex along generalized geodesics and sufficiently strong relative to the price. This extends the mean-field analysis from relative entropy to weight decay and to finite networks. Relative entropy adds parameter noise and a pull toward a prior, whereas weight decay provides only the pull. Action regularization bounds changes in failure risk by the relative entropy to a reference policy. The bounds are evaluated on an exact maintenance benchmark, a fuel-tank controller, a solvable flow and a benchmark-suite task.
查看此版本解读 →查看此版本原文 ↗v3 · 2026-10-27 22:54
The Price of Failure Risk: Clipped Barrier Policy Gradients with Convex Regularization
Many operations run on a budget that must rarely run out, such as a wear allowance. A wrapper keeps the remaining budget in the state, subtracts a barrier that grows as the budget shrinks and clips the combined reward from below at -m, and a standard policy-gradient learner trains unchanged. The clip level m is a price of failure risk, since the trained value splits exactly into utility before failure, the cost of a margin and the price times the risk, so whatever policy training returns earns the most such utility net of that cost among policies with no greater risk, up to its optimization error. Its risk exceeds a comparison policy's by at most order 1/m when charged costs stay bounded, and value or validation data certify it. The main theoretical result is exponential convergence of the population training flow under any parameter regularizer convex along the motions of the network's units and strong enough against the price, biased toward the prior policy. This extends mean-field convergence of policy gradients from relative entropy to weight decay, which covers continuous-time training of finite networks. Relative entropy adds noise that lets learning leave flat regions, weight decay pulls the parameters toward a reference, and action regularization bounds the risk change by the distance to a trusted rule. Experiments on an exact maintenance benchmark, a fuel-tank controller, a solvable flow and a benchmark-suite task measure the bounds' slack. We state when another method is better, without claiming this one outperforms them.
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