We first address questions that might arise in response to the main text. That is, if Alice chooses a SOAP, PO, or TO for Bob to learn to solve, when can Alice determine Bob has solved the task? A: Bob can be said to be doing better on a given task if his behavior improves, as is typical in evaluating behavior under reward. The difference with SOAPs, POs, and TOs is that we measure improvement relative to the task rather than reward. For instance, given a SOAP, we might say that Bob has solved the task once he has found one of the good policies, and we might measure Bob's progress on a task in terms of the distance of his greedy policy to one of the good policies (as done in our learning experiments). The same reasoning applies to POs and TOs: Bob is doing better on a task in so far as his greedy policy (or trajectories) is (are) higher up the ordering. That is, the studied reward functions must be a function of s, (s,a), or (s,a,s0). A: Indeed, as discussed in our introduction, our goal is to examine the expressivity of Markov rewards in the context of finite MDPs.

This technical note studies the reliability limits of LLM-based multi-agent planning as a delegated decision problem. We model the LLM-based multi-agent architecture as a finite acyclic decision network in which multiple stages process shared model-context information, communicate through language interfaces with limited capacity, and may invoke human review. We show that, without new exogenous signals, any delegated network is decision-theoretically dominated by a centralized Bayes decision maker with access to the same information. In the common-evidence regime, this implies that optimizing over multi-agent directed acyclic graphs under a finite communication budget can be recast as choosing a budget-constrained stochastic experiment on the shared signal. We also characterize the loss induced by communication and information compression. Under proper scoring rules, the gap between the centralized Bayes value and the value after communication admits an expected posterior divergence representation, which reduces to conditional mutual information under logarithmic loss and to expected squared posterior error under the Brier score. These results characterize the fundamental reliability limits of delegated LLM planning. Experiments with LLMs on a controlled problem set further demonstrate these characterizations.

In many real-world decision problems there is partially observed, hidden or latent information that remains fixed throughout an interaction. Such decision problems can be modeled as Latent Markov Decision Processes (LMDPs), where a latent variable is selected at the beginning of an interaction and is not disclosed to the agent initially. In last decade, there has been significant progress in designing learning algorithms for solving LMDPs under different structural assumptions. However, for general LMDPs, there is no known learning algorithm that provably matches the existing lower bound. We effectively resolve this open question, introducing the first sample-efficient algorithm for LMDPs without . Our result builds off a new perspective on the role off-policy evaluation guarantees and coverage coefficient in LMDPs, a perspective, which has been overlooked in the context of exploration in partially observed environments. Specifically, we establish a novel off-policy evaluation lemma and introduce a new coverage coefficient for LMDPs. Then, we show how these can be used to derive near-optimal guarantees of an optimistic exploration algorithm. These results, we believe, can be valuable for a wide range of interactive learning problems beyond the LMDP class, and especially, for partially observed environments.

This paper introduces a model-based reinforcement learning (MBRL) framework that incorporates the underlying decision problem in learning the transition model of the environment. This is in contrast with conventional approaches to MBRL that learn the model of the environment, for example by finding the maximum likelihood estimate, without taking into account the decision problem. Value-Aware Model Learning (VAML) framework argues that this might not be a good idea, especially if the true model of the environment does not belong to the model class from which we are estimating the model. The original VAML framework, however, may result in an optimization problem that is difficult to solve. This paper introduces a new MBRL class of algorithms, called Iterative VAML, that benefits from the structure of how the planning is performed (i.e., through approximate value iteration) to devise a simpler optimization problem. The paper theoretically analyzes Iterative VAML and provides finite sample error upper bound guarantee for it.

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

In this paper, we develop efficient parameterized algorithms for regimes between these two extremes.

In a standard view of the reinforcement learning problem, an agent's goal is to efficiently identify a policy that maximizes long-term reward.

These metrics admit differentiable sample estimates, making it easy to incorporate a calibration objective into empirical risk minimization.