Unbiased Canonical Set-Valued Oracles Via Lattice Theory

Agentic systems often fail not by being entirely wrong, but by being too precise: a response may be generally useful while particular claims exceed what the evidence supports. We study this failure mode as overcommitment control and introduce compositional selective specificity (CSS), a post-generation layer that decomposes an answer into claims, proposes coarser backoffs, and emits each claim at the most specific calibrated level that appears admissible. The method is designed to express uncertainty as a local semantic backoff rather than as a whole-answer refusal. Across a full LongFact run and HotpotQA pilots, calibrated CSS improves the risk-utility trade-off of fixed drafts. On the full LongFact run, it raises overcommitment-aware utility from 0.846 to 0.913 relative to the no-CSS output while achieving 0.938 specificity retention. These results suggest that claim-level specificity control is a useful uncertainty interface for agentic systems and a target for future distribution-free validity layers.

Many signal processing systems ultimately exist to {act}. Whenever the state variable that determines the action to be taken by a decision maker, or agent, is uncertain, the way that uncertainty is represented decides how well the agent performs and how much its performance can be trusted. This lecture note develops, from first principles and within a single decision-theoretic setting, the link between the {objective} and the knowledge of an agent and the form of uncertainty representation that is sufficient to act optimally. To start, assuming a known environment distribution, we show that a risk-neutral agent needs the posterior distribution over the state, whereas a risk-averse agent can rely without loss of optimality on a {prediction set} and a worst-case decision rule. We then turn to the case in which the environment is unknown, and identify three complementary approaches to address the resulting epistemic uncertainty: calibration of a fixed predictor, credal (ambiguity) sets with distributionally robust optimization, and Bayesian inference over model parameters. The common thread is that reliable decisions require an uncertainty representation matched to the decision objective and to the knowledge profile of the agent, together with a guarantee that certifies the utility the agent will actually obtain.

Counterfactual recourse aims to provide actionable feature changes that would alter an unfavorable decision made by a predictive model. In practice, affected individuals often benefit from multiple feasible alternatives rather than a single optimal explanation. A natural way to produce such alternatives is to prompt large language models (LLMs). However, prompting incurs a practical constraint: the number of LLM calls is often the dominant computational and economic cost. Together, the need for multiple alternatives and this cost constraint shift the problem from finding a single high-quality counterfactual to efficiently generating a set of oracle-validated counterfactuals under a fixed LLM-call budget. In this work, we study counterfactual recourse generation in the LLM-agentic setting as a fixed-budget search problem and propose Comp-MCTS, an agentic tree-search framework that maximizes the yield of unique, oracle-validated counterfactuals under this budget while maintaining favorable quantity--quality trade-offs. Comp-MCTS allocates the budget toward novel intervention directions via LLM-based proposal generation, oracle validation, and compression-guided pruning, in a training-free, oracle-only setting. Experiments on four real-world tabular datasets show that Comp-MCTS substantially outperforms single-candidate LATS-style baselines in the yield of unique, oracle-validated counterfactuals, and offers favorable quantity--quality--efficiency trade-offs against stronger multi-candidate variants: comparable or higher yield at similar or lower oracle-evaluation cost on three of four datasets, plus competitive proximity, sparsity, and novelty.