Computing an approximately optimal policy with high probability in this case is known as PAC RL with a generative model.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call strong verification. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. We formalize this tension through weak--strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification. We introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, we show that optimal policies admit a two-threshold structure and that calibration and sharpness govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors without assumptions on the query stream, the language model, or the weak verifier.

Neural Information Processing Systems http://nips.cc/

Markov decision processes (MDPs) often suffer from the sensitivity issue under model ambiguity. In recent years, robust MDPs have emerged as an effective framework to overcome this challenge. Distributionally robust MDPs extend the robust MDP framework by incorporating distributional information of the uncertain model parameters to alleviate the conservative nature of robust MDPs.

Neural Information Processing Systems http://nips.cc/

Hedonic Games (HGs) are a classical framework modeling coalition formation of strategic agents guided by their individual preferences.

Let = argm 2 CF ( )denote (2). T ( )+ log ( 1/ )+( 1) log ( 1/ ) log ( ) 1 , (5) where ( )isthe RDPof 2. Convergence:IfwerunAcldpwith t = DGpt, whereG2 = max{d1 Substitutingtheboundon4 into Lemma 2 together manipulationgivesproves Theorem 1; see Appendix E.2 fordetails.