Zero Collapse: A Failure Mode of Policy Gradient Methods in Discontinuous Reward Environments
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| Format: | Preprint |
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2026
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| _version_ | 1866911731335299072 |
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| author | Kumar, Nishant Viqueira, Enrique Areyan Greenwald, Amy |
| author_facet | Kumar, Nishant Viqueira, Enrique Areyan Greenwald, Amy |
| contents | Bidding in repeated auctions is a central challenge for reinforcement learning (RL), combining continuous control with the strategic complexities of digital advertising. While policy gradient and value-based methods seem well-suited for these settings, they often struggle with the discontinuous, "cliff-like" nature of auction reward landscapes. In a first-price auction, for example, a bidder receives zero reward until they cross a specific threshold, after which the reward decreases as the bid increases. This creates a landscape of flat, zero-reward regions separated by sharp boundaries.
We identify a fundamental failure mode in this setting termed "zero collapse." We show that stochastic exploration and gradient-based updates can cause policies to overshoot optimal high-reward regions and enter flat, zero-reward regimes. Once there, the lack of an informative gradient signal makes recovery extremely sample-inefficient, effectively trapping the agent. We find that actor-critic methods are particularly susceptible, as biased value estimates can accelerate this movement toward unstable regions.
Our contributions include: (1) a mechanistic explanation of how discontinuous rewards lead to vanishing signals and zero collapse; (2) an analysis of the interaction between policy stochasticity and step size; and (3) an empirical demonstration of this phenomenon across REINFORCE and actor-critic variants. We propose practical mitigation strategies involving initialization and architectural choices to improve stability. Finally, we introduce a formal RL framework for auction environments highlighting their unique structural properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_30896 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zero Collapse: A Failure Mode of Policy Gradient Methods in Discontinuous Reward Environments Kumar, Nishant Viqueira, Enrique Areyan Greenwald, Amy Machine Learning Bidding in repeated auctions is a central challenge for reinforcement learning (RL), combining continuous control with the strategic complexities of digital advertising. While policy gradient and value-based methods seem well-suited for these settings, they often struggle with the discontinuous, "cliff-like" nature of auction reward landscapes. In a first-price auction, for example, a bidder receives zero reward until they cross a specific threshold, after which the reward decreases as the bid increases. This creates a landscape of flat, zero-reward regions separated by sharp boundaries. We identify a fundamental failure mode in this setting termed "zero collapse." We show that stochastic exploration and gradient-based updates can cause policies to overshoot optimal high-reward regions and enter flat, zero-reward regimes. Once there, the lack of an informative gradient signal makes recovery extremely sample-inefficient, effectively trapping the agent. We find that actor-critic methods are particularly susceptible, as biased value estimates can accelerate this movement toward unstable regions. Our contributions include: (1) a mechanistic explanation of how discontinuous rewards lead to vanishing signals and zero collapse; (2) an analysis of the interaction between policy stochasticity and step size; and (3) an empirical demonstration of this phenomenon across REINFORCE and actor-critic variants. We propose practical mitigation strategies involving initialization and architectural choices to improve stability. Finally, we introduce a formal RL framework for auction environments highlighting their unique structural properties. |
| title | Zero Collapse: A Failure Mode of Policy Gradient Methods in Discontinuous Reward Environments |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.30896 |