An LLM application often sells or internally allocates several service products: a small or premium model, a short or long token cap, and possibly multiple posted prices. The operational decision is not merely which model answers a prompt. A price changes purchase probability, a token cap changes both user value and the tail of resource consumption, and accepted requests compete for shared compute and premium-model capacity. Demand and output length are initially uncertain, while an offline model may provide useful but imperfect predictions. We formulate sequential pricing and admission with stochastic resource consumption. Each arriving request belongs to an observable segment. The platform chooses a product--price pair or makes no offer; purchase, revenue, and resource use are then random. An offline predictor supplies a uniform, validated error radius for every segment--product cell. We propose Prediction-Clipped UCB (PCUCB), which intersects the offline prediction interval with an online confidence interval, evaluates products using resource shadow prices, and reserves a sample-path envelope before commitment. The prior gives a fast start when accurate, while online learning protects the platform when predictions are coarse. The analysis is modular. On a simultaneous confidence event, regret against a buffered fluid benchmark is bounded by a pacing term plus the cumulative diameter of the intersected intervals. For $J$ segment-product cells and prediction radius $\varepsilon$, this yields \[ \widetilde O\left( \sqrt{T}+(1+\barΛ) \min\{T\varepsilon,\sqrt{JT}\} \right), \] where $\barΛ$ bounds operational shadow prices. Thus the algorithm smoothly interpolates between an almost full-information regime and learning from scratch. Hard feasibility holds on every sample path through reservation envelopes.
In online retailing, when a product sells out, a retailer often sees only the units sold, not how many customers would have bought it had inventory been available. However, the inventory level determines how much demand is revealed, and this information can influence subsequent decisions and future profits. We study an online selling problem in which, in each round, the seller observes a market context and then makes pricing and stocking decisions based on censored sales data from previous rounds. The challenge is to learn a context-dependent pricing and stocking policy without assuming a particular formula for demand or observing realized profit. To overcome this difficulty, we propose a Mean-Calibrated Kernel UCB (MCK-UCB) algorithm that turns each incomplete sales record into a reliable guide for both inventory and price decisions, using data from past rounds with similar market conditions. This design allows us to learn while serving customers, without a separate exploration phase or the need to recover all demand hidden by stockouts. We prove the minimax optimality of the proposed algorithm, with strictly faster rates when expected profit varies more smoothly with price. Comprehensive numerical experiments have been conducted to confirm the effectiveness of the proposed algorithm.
Short observational pricing panels often contain many observations but few distinct price movements. We evaluate the inferential consequences of this sparsity in a synthetic data-generating process by separating estimation error into uncertainty conditional on a realized price trajectory and variation across alternative trajectories. In baseline simulations, this across-design component accounts for 97.6% of estimation error variance for a gradient-boosted specification, causing coverage shortfalls driven by design-specific centering error that standard within-panel resampling and cluster-robust procedures fail to capture. Three main results organize the analysis. First, across-design dispersion follows the empirical relation sigma_b approx 0.182 V^(-0.271), where V = n_moves * magnitude^2, with -0.271 treated as a simulation regularity. Second, adding regions sharing a common price path improves nuisance estimation but creates no independent price trajectories; only averaging across units with independent design errors reduces across-design standard deviation at the sqrt(k) rate. Third, a Paule-Mandel variance component estimated across independently priced units increases empirical coverage under homogeneity from 0.469 to 0.931. Broadly, improving inference in passive panels requires generating independent identifying variation, such as through controlled regional randomization. Finally, an application to scanner data (Dominick's Finer Foods, Soft Drinks) confirms these findings: nominal price zones and products behave as a small fraction of their count in independent design draws, yielding between-unit dispersion intervals far wider than conventional within-panel bootstraps.
Youssef Drissi, Markus Ettl, Shivaram Subramanian +2cs.LG
We introduce COAT (Counterfactual Optimal Action Tree), a framework for learning interpretable prescriptive policies from observational data. COAT combines counterfactual outcome estimation with large-scale mixed-integer optimization, using column generation to translate causal predictions into feasible, transparent decisions under business and regulatory constraints. We apply COAT to airline ancillary pricing, a setting characterized by complex business rules and limited experimental flexibility. In a 17-week field pilot with a major global airline, COAT increased upsell revenue per booking by 6.9%, with the airline projecting \$50-\$150 million in incremental annual premium seat revenue across eligible domestic markets. The success of the pilot led to scaled adoption and informed broader AI-driven decision initiatives within the organization.
On a platform with many sellers, should a pricing algorithm explicitly model competitors' prices when learning demand? Classical learning arguments suggest an affirmative answer: ignoring competitors induces model misspecification and inefficiency. In contrast, recent work on algorithmic collusion suggests that strategic obliviousness -- deliberately ignoring competitor prices -- may facilitate collusive outcomes and improve profits. We study this modeling choice in a stylized competitive market with unknown noisy demand, in which multiple sellers repeatedly set prices and estimate demand via iterated least squares, and either incorporate competitors' prices into their demand models (informed) or ignore them (oblivious). We first show that, relative to a monopolist, an oblivious seller in a competitive market must explore more aggressively to compensate for the loss of dynamic competitor information. Building on this insight, we characterize market dynamics when all sellers are oblivious and show that prices converge to the competitive outcome under sufficient exploration, while a continuum of pseudo-equilibria arises when exploration decays. Analyzing the resulting price trajectories, we uncover an excursion phenomenon that gives rise to transient collusive patterns that dissipate as learning progresses. In markets with both oblivious and informed sellers, the informed strictly out-earn the oblivious. Read as a strategy game, the modeling choice has a unique Nash equilibrium: the all-informed market, in which prices converge to the competitive outcome efficiently. Overall, our results indicate that collusive patterns are not robust and are not sustained by oblivious modeling; therefore, incorporating competitor information, together with sufficient price exploration, remains a reliable strategy for sellers in competitive markets.