automated decision system builders

Abstract: We study personalized LLM routing, where a router selects among heterogeneous models with different costs and capabilities. The router must minimize cumulative inference cost while ensuring reliable realized response quality, even though user preferences are unknown and must be learned from feedback during deployment. We formulate this problem as a constrained contextual bandit and develop an algorithm that learns preferences while balancing cost and quality. Under a logistic preference model and a strict-feasibility condition, we establish sublinear expected cost regret relative to an optimal stationary randomized contextual oracle and a high-probability guarantee on realized cumulative satisfaction. The framework extends beyond LLM routing to broader online model-selection problems with reliability requirements.

Abstract: Calibrating a conformal prediction set at each early exit does not preserve coverage once a data-dependent exit is selected. We construct one terminal path score from prefix maxima, calibrate a single split-conformal quantile, and return nested prefix sets that all contain the valid terminal set. The guarantee is selection-safe without an alpha/L correction and holds simultaneously for every post-calibration label-free stopping policy that preserves terminal-set containment. We also bound the efficiency cost of the path maximum by the empirical tail of the early-over-terminal score excess. Across eight encoder task-backbone cells, pathwise selection attains macro coverage 0.901 versus 0.814 for naive layerwise selection, with average set size 1.41 and latency fraction 0.71. On CIFAR-100 with a 24-exit ViT-L/16 (n_cal=500), first-eligible stopping at budget b=4 attains coverage 0.902, set size 2.76, and latency fraction 0.57, and the same calibration supports deployment-time budget changes without refitting. In a joint exit-count/calibration-size sweep at n=100, pathwise set size moves only from 3.02 to 3.11 as exits increase from 4 to 24, while Bonferroni degenerates to the full label space for 12 or more exits. Paired comparison against MinSE valid selection at (n,L)=(100,24) gives a set-size difference of 0.80 [0.47, 1.13]. Full-vocabulary decoder experiments remain a negative boundary, with sets of 7,162-9,620 tokens. Pathwise calibration is most useful when candidate exits are many relative to calibration size, when budgets change after calibration, and when shallow heads return actionable sets.

Abstract: Signals that predict whether a chain-of-thought (CoT) trace is correct are compared by AUC, but deploying one requires a threshold with a guarantee. We ask what distribution-free selective guarantees deliver for CoT verifiers at realistic calibration budgets of tens to a few hundred labelled problems, using seven open models, five verifier signals and 37,000 graded traces. The central observation is validity by abstention: an $(α,δ)$-valid procedure that issues a certificate with probability $P_{\rm fire}$ bounds the failure probability of an issued certificate only by $δ/P_{\rm fire}$, so a certificate that rarely fires can be valid and wrong every time it is used. In a simulation with known risk the standard certificate fails in at most 0.3% of calibration draws but in up to 69% of those in which it fires. A certification floor and a lattice condition for Benjamini-Hochberg conformal selection explain why certificates abstain at these budgets, and the data bear them out: the standard certificate returns nothing or a large accepted set, and an unreadable residual-stream probe buys two to three times the coverage of the readable signals, an edge a cross-fitted reconstruction cannot recover linearly from the readable features. We then give a floor-started fixed-sequence certificate, valid without monotonicity assumptions, that covers more than the Bonferroni certificate on every model-signal pair and raises coverage at the non-vacuous target $0.75π_0$ from 0.05 to 0.16, although the floor keeps absolute coverage small. Finally, a certificate cannot see what matters after deployment: under benchmark shift the error among accepted traces tracks the new task's base error, and under best-of-$n$ selection against the verifier it rises past the target while the empirical failure frequency stays below $δ$, because abstention absorbs the failures.