自由推断维度：假设混合下零碰撞导航的复杂度度量
The Free Inference Dimension: Complexity Measure for Zero-Collision Navigation under Hypothesis Mixtures
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中文总结 AI 辅助
本文提出自由推断维度dFI，度量值混合智能体在假设混合下零碰撞导航的复杂度，证明其小于VC维，并验证混合策略的最优性。
中文摘要 AI 辅助
Solomonoff归纳将预测视为对可计算假设的混合，通常会导致对真实环境的识别。在我们先前的工作中，在一个具有嵌套约束族的有限元强化学习设置中，我们观察到一个不同的机制：一个值混合（VM）智能体能够在无需识别真实环境的情况下实现接近最优的零碰撞导航，我们将这一现象称为自由推断。该机制持续存在直至一个尖锐的密度阈值，超过该阈值后性能下降，后验众数选择（PMS）变得更为可取。我们通过自由推断维度dFI(S,N)形式化了这一行为，该维度是一个组合度量，衡量VM智能体在保持轨迹连贯性的同时能够处理的环境复杂度。我们证明了dFI严格小于VC维度，并与Natarajan维度相差一个路径长度因子，从而捕捉了不可分解损失的成本。一种PAC风格的松弛方法产生了由dFI^(epsilon,delta)驱动的泛化界。我们还定义了一个互补的PMS识别维度，并表明一种混合策略——在首次碰撞前进行平均，然后切换到选择——是最优的，这与Littlestone型维度的联系得到了网格世界实验的支持。
英文摘要
Solomonoff induction frames prediction as a mixture over computable hypotheses, typically leading to identification of the true environment. In a finite meta-reinforcement learning setting with nested constraint families, in our previous work, we observe a different regime: a value-mixture (VM) agent achieves near-optimal, zero-collision navigation without identifying the true environment, a phenomenon we call Free Inference. This regime persists up to a sharp density threshold, beyond which performance degrades and posterior-mode selection (PMS) becomes preferable. We formalize this behavior via the Free Inference dimension dFI(S,N), a combinatorial measure of the environmental complexity a VM agent can handle while preserving trajectory coherence. We prove dFI is strictly smaller than the VC-dimension and relates to the Natarajan dimension up to a path-length factor, capturing the cost of non-decomposable loss. A PAC-style relaxation yields generalization bounds driven by dFI^(epsilon,delta). We also define a complementary PMS identification dimension and show that a hybrid strategy---averaging until the first collision, then switching to selection---is optimal, with links to Littlestone-type dimensions supported by grid-world experiments.
发表机构
- PUC-Rio（里约热内卢天主教大学）
- Instituto Militar de Engenharia（军事工程学院）
机构由 AI 辅助整理，请以论文原文为准。
