Sign-Separated Asymmetric Finite-Time Error Analysis of Q-Learning

Donghwan Lee

Home/Archive/arXiv

arXiv · 2605.16103

Sign-Separated Asymmetric Finite-Time Error Analysis of Q-Learning

Donghwan Lee

View original source ↗Read source document ↗Export metadata ↓

Abstract

Q-learning is known to suffer from overestimation bias: because the Bellman update maximizes noisy or imperfect action-value estimates, positive errors can be selected and propagated, causing learned values to exceed the true optimal values. This bias can slow learning, degrade policy quality, and make value estimates unreliable. Although the convergence of Q-learning has been studied extensively, convergence theory that explicitly reflects this overestimation mechanism remains limited. This paper studies the asymmetric convergence behavior of Q-learning induced by overestimation bias. We decompose the Q-learning error into its componentwise positive and negative parts and derive separate finite-time rates for the two components. The resulting certificates can assign a slower exponential envelope to the positive component than to the negative component. This rate separation provides indirect theoretical evidence for max-induced overestimation: positive errors can be amplified through the maximization step, whereas negative errors admit a sharper comparison with an optimal-policy system. The separation is a difference between upper bounds, so it need not hold for every realized Q-learning trajectory. Nevertheless, we construct examples in which the predicted asymmetry appears in the actual trajectory. The analysis gives deterministic and stochastic constant-step-size bounds and clarifies how overestimation enters the switching-system dynamics of Q-learning.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Donghwan Lee. 2026-07-05. Sign-Separated Asymmetric Finite-Time Error Analysis of Q-Learning. https://arxiv.org/abs/2605.16103

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Memory-Free Continual Learning with Null Space Adaptation for Zero-Shot Vision-Language Models

Pre-trained vision-language models (VLMs), such as CLIP, have demonstrated remarkable zero-shot generalization, enabling deployment in a wide range of real-world tasks without additional task-specific training. However, in real deployment scenarios with evolving environments or emerging classes, these models inevitably face distributional shifts and novel tasks. In such contexts, static zero-shot capabilities are insufficient, and there is a growing need for continual learning methods that allow models to adapt over time while avoiding catastrophic forgetting. We introduce NuSA-CL (Null Space Adaptation for Continual Learning), a lightweight memory-free continual learning framework designed to address this challenge. NuSA-CL employs low-rank adaptation and constrains task-specific weight updates to lie within an approximate null space of the model's current parameters. This strategy minimizes interference with previously acquired knowledge, effectively preserving the zero-shot capabilities of the original model. Unlike methods relying on replay buffers or costly distillation, NuSA-CL imposes minimal computational and memory overhead, making it practical for deployment in resource-constrained, real-world continual learning environments. Experiments show that our framework not only effectively preserves zero-shot transfer capabilities but also achieves highly competitive performance on continual learning benchmarks. These results position NuSA-CL as a practical and scalable solution for continually evolving zero-shot VLMs in real-world applications.

cs.AI↗

arXiv2026

VeRA: Renewing Reasoning Benchmarks with Executable Specifications

Reasoning benchmarks need renewal along two axes: freshness and headroom. VeRA makes both executable and auditable by turning each item into a task family: a natural-language template, an input generator, and a deterministic answer program. VeRA-E draws fresh instances within a family; VeRA-H modifies the family toward harder tasks; and VeRA-H Pro selects one judge-ranked candidate from up to five validated proposals per seed. Execution checks, seed anchoring, answer discrimination, and independent human solving validate specifications and items. Accepted programs generate further labeled instances through local computation. Across 16 models, AIME-2024 accuracy decreases from 84.46% on seeds to 70.25% on VeRA-E variants, exposing a gap between fixed-item success and fresh-instance robustness. On AIME-2024-II, the human-audited VeRA-H Pro release lowers accuracy from 84.91% to 58.57%. Across the three hardening sources, H Pro has lower mean accuracy than H. On AMO-Bench, both releases average higher accuracy than the seeds under the evaluated budget. Initial auditing accepts 75.4% of hardened candidates; targeted repair raises usable yield to 95.1%. Executable families thus support repeatable benchmark renewal, with validation improving task quality and selection shaping the delivered challenge.

cs.AI↗

arXiv2026

When can we trust untrusted monitoring? A safety case sketch across collusion strategies

AIs are increasingly being deployed with greater autonomy and capabilities, which increases the risk that a misaligned AI may be able to cause catastrophic harm. Untrusted monitoring -- using one untrusted model to oversee another -- is one approach to reducing risk. Justifying the safety of an untrusted monitoring deployment is challenging because developers cannot safely deploy a misaligned model to test their protocol directly. In this paper, we develop upon existing methods for rigorously demonstrating safety based on pre-deployment testing. We relax assumptions that previous AI control research made about the collusion strategies a misaligned AI might use to subvert untrusted monitoring. We develop a taxonomy covering passive self-recognition, causal collusion (hiding pre-shared signals), acausal collusion (hiding signals via Schelling points), and combined strategies. We create a safety case sketch to clearly present our argument, explicitly state our assumptions, and highlight unsolved challenges. We identify conditions under which passive self-recognition could be a more effective collusion strategy than those studied previously. Our work builds towards more robust evaluations of untrusted monitoring.

cs.AI↗