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In-Context Learning for Data-Driven Censored Inventory Control

This paper proposes In-Context Generative Posterior Sampling (ICGPS), a framework that leverages meta-trained generative models to perform oracle actions on learned latent demand completions, thereby achieving sublinear Bayesian regret and robustness to prior mismatch in data-driven censored inventory control problems like the repeated newsvendor.

Original authors: Sohom Mukherjee, Anh-Duy Pham, Richard Pibernik, Yunbei Xu

Published 2026-05-15

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CC BY 4.0

Original authors: Sohom Mukherjee, Anh-Duy Pham, Richard Pibernik, Yunbei Xu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are running a lemonade stand. Every morning, you have to decide how many cups of lemonade to make before you know how many people will actually show up.

If you make too few, you run out of lemonade (a "stockout"). If you make too many, you waste money on leftover lemonade. This is the classic "Newsvendor Problem."

Now, imagine a twist: You can never see the true demand.

If you make 10 cups and 15 people show up, you sell 10 and run out. You know demand was at least 10, but you don't know if it was 11, 20, or 100. The data is "censored" (cut off).
If you make 20 cups and only 5 people show up, you see exactly 5. The data is clear.

The challenge is: How do you learn to make the perfect amount of lemonade when your most valuable learning moments (running out of stock) hide the truth from you?

The Old Ways vs. The New Way

The paper explains that previous methods tried to solve this in two ways, both with flaws:

The "Gut Feeling" Method (Parametric Thompson Sampling): You guess a specific shape for the demand curve (e.g., "It's always a bell curve"). If your guess is wrong, your whole strategy fails.
The "Backfill" Method (Offline Imputation): You try to guess the missing numbers after the fact using old data. But this often fails when you try to use it in real-time, live situations.

The authors propose a new approach called In-Context Generative Posterior Sampling (ICGPS).

The Creative Analogy: The "Dreaming" Chef

Think of the new method as a Chef who learns by dreaming.

Instead of trying to guess a mathematical formula for demand, the Chef has a powerful Dream Generator (a modern AI model).

The Training Phase (Offline): The Chef watches thousands of videos of other lemonade stands. Some days they ran out; some days they had leftovers. The Chef learns to fill in the blanks. If a video shows a stand selling 10 cups and then running out, the Chef's Dream Generator learns to imagine plausible scenarios: "Maybe 12 people came? Maybe 15? Maybe 50?" It learns to fill in the missing demand numbers in a way that makes sense with the history.
The Dreaming Phase (Online): Every morning, before making lemonade, the Chef doesn't just guess. They dream up a complete day.
- They look at their history (what happened yesterday, the day before).
- They ask the Dream Generator: "Given what happened before, what could the full day have looked like?"
- The Generator creates a complete, fake day where the demand is fully revealed (no censoring). It fills in the missing numbers with plausible guesses.
The Decision: The Chef looks at this dreamed-up complete day and asks, "If this were real, how much lemonade would I have made to be perfect?" They take that action.
The Reality Check: They make the lemonade, sell it, and see the actual result (which might be censored again). They add this new real data to their history and repeat the process.

The magic is that the Chef doesn't need to retrain the Dream Generator every day. They just use the context of the current day's history to guide the dream. This is called "In-Context Learning."

The Secret Sauce: ChronosFlow

To make this "Dream Generator" fast and accurate, the authors built a specific architecture called ChronosFlow.

The Backbone (Chronos): Think of this as a super-smart librarian who has read every time-series book ever written. It understands patterns in time (like "lemonade sales go up on hot days").
The Head (Flow): This is the part that actually fills in the missing numbers. It's designed to respect the rules of the game. If the history says "We sold out at 10 cups," the Dream Generator is forced to imagine a demand higher than 10. It can't imagine a demand of 5 if we know we ran out.

What the Paper Found

The authors tested this "Dreaming Chef" against the old methods:

It matches the experts: When the demand follows a simple, predictable pattern, the Dreaming Chef performs just as well as the best theoretical experts (Thompson Sampling).
It's robust: If the real world changes (e.g., the demand pattern shifts from a bell curve to something weird), the Dreaming Chef adapts quickly. The old "Gut Feeling" methods often crash because their formulas were wrong.
It handles heavy censorship: When the lemonade stand runs out of stock a lot (hiding the true demand), the Dreaming Chef shines. It uses its training to guess the missing numbers better than methods that try to guess without a "dream" generator.
Real-world success: They tested this on real sales data from a "SuperStore." Even with messy, real-world data where stockouts were frequent, the Dreaming Chef (specifically the "Meta" version, which learned from other stores first) made better decisions than the competition.

The Bottom Line

The paper claims that by treating missing data as a "dream" that can be generated by an AI, rather than a math problem to be solved with a rigid formula, we can make better inventory decisions. The system learns from past experiences, fills in the gaps of the present, and makes a decision based on a "what-if" scenario that respects the rules of the game.

Key Takeaway: You don't need to know the exact future to make a good decision; you just need to be able to imagine a few plausible futures that fit the clues you have, and act as if the best one is real.

Technical Summary: In-Context Learning for Data-Driven Censored Inventory Control

Problem Statement

The paper addresses the Repeated Newsvendor (R-NV) problem, a canonical operational decision-making scenario characterized by decision-dependent uncertainty and right-censoring. In this setting, a decision-maker selects an order quantity $X_t$ each period. The latent demand $D_t$ is only partially observed: if $D_t \le X_t$ , the exact demand is observed; if $D_t > X_t$ (a stockout), only the sales figure $X_t$ and a stockout indicator are observed. This censoring creates a fundamental exploration-exploitation tension: conservative ordering minimizes immediate holding costs but increases censoring, thereby hindering future learning about the demand distribution.

Existing approaches face significant limitations:

Parametric Thompson Sampling (TS): While theoretically powerful, TS relies on a correctly specified prior. In practice, prior mismatch can lead to severe performance degradation.
Offline Imputation: Methods that attempt to de-censor demand (e.g., via Kaplan-Meier estimators) are typically confined to offline settings and lack theoretical guarantees for online sequential decision-making.

The authors aim to bridge this gap by developing an online learning algorithm that provides performance guarantees in continuous action spaces without requiring a known parametric prior, while effectively handling the missing data structure induced by censoring.

Methodology: In-Context Generative Posterior Sampling (ICGPS)

The proposed solution, In-Context Generative Posterior Sampling (ICGPS), reframes the learning problem through a "missing data" perspective. Instead of estimating parameters, the algorithm treats unobserved demand components as missing outcomes that can be "completed" consistent with the observed feedback mechanism.

Core Framework

Offline Meta-Training: A conditional generative model is trained on historical data (offline episodes) to learn a completion kernel. This model learns to sample plausible full demand trajectories $D_{1:T}$ $D_{1 : T}$ conditioned on the observed history $H_{t-1}$ $H_{t - 1}$ (which includes actions, sales, and censoring indicators).
- Loss Function: The model is trained using a censoring-aware negative log-likelihood. Uncensored observations contribute a density term, while censored observations contribute a survival term (analogous to survival analysis).
Online In-Context Adaptation: During deployment, the model is frozen. At each time step $t$ $t$ , the algorithm:
- Samples a complete demand trajectory $\tilde{D}^{(t)}_{1:T}$ from the learned conditional distribution $p_\theta(\cdot | H_{t-1})$ .
- Constraint Enforcement: Crucially, the sampling process enforces hard consistency constraints. If a past period $s < t$ was censored (stockout), the sampled demand $\tilde{D}_s$ must satisfy $\tilde{D}_s > X_s$ . This is achieved via tail-conditioning (sampling from the conditional tail of the distribution).
- Oracle Action: The algorithm computes the "oracle" action for the sampled trajectory. For the R-NV problem, this is the empirical $\gamma$ -quantile (where $\gamma = b/(b+h)$ is the critical fractile) of the completed demand sequence.
- The decision-maker executes this action, observes new censored feedback, and updates the context history without updating model parameters.

Architecture: ChronosFlow

To instantiate ICGPS practically, the authors propose ChronosFlow, a modular architecture:

Backbone: A frozen Chronos-2 time-series transformer (pretrained on massive datasets) that extracts in-context quantile features from the history.
Head: A lightweight Conditional Normalizing Flow (CNF) that maps the context vector to a conditional distribution over demand. The CNF allows for exact inverse transform sampling, facilitating the enforcement of censoring constraints (tail conditioning) during online generation.

Theoretical Contributions

The paper provides a rigorous Bayesian regret analysis that decomposes the performance of the deployed ICGPS policy into two terms:

Ideal Benchmark Regret (Term I): The regret of an ideal Thompson Sampling policy that uses the true completion kernel.
- The authors prove that for the R-NV problem, the censored feedback structure can be reduced to Bandit Convex Optimization (BCO) with scalar actions.
- By leveraging recent results on TS for BCO (Bakhtiari et al., 2025), they establish that the ideal benchmark achieves a sublinear Bayesian regret of $\tilde{O}(\sqrt{T})$ . This is presented as the first Bayesian regret analysis for TS in the R-NV setting using the information-ratio framework.
Deployment Penalty (Term II): The additional regret incurred by using a learned completion model instead of the true one.
- The authors derive a bound showing this penalty scales as $\sqrt{T} \times \sqrt{\Delta_{\text{comp}}}$ , where $\Delta_{\text{comp}}$ is the on-policy completion mismatch (KL divergence between true and learned trajectory completions).
- Crucially, they show that under max-order coverage (the policy occasionally orders the maximum capacity to reveal tail demand) and self-contraction (errors in autoregressive generation decay over time), the completion mismatch is controlled by the observable predictive mismatch (the offline training loss).
- This establishes a theoretical link: high-quality offline predictive fit translates to low online regret.

Experimental Results

The authors evaluate ChronosFlow-ICGPS across synthetic and real-world datasets:

Sanity Check (Correct Specification): In i.i.d. Weibull demand settings, ChronosFlow-ICGPS matches the performance of a correctly specified parametric Thompson Sampling baseline across various service levels ( $\gamma$ ), validating that the generative approach recovers classical behavior when the model is well-specified.
Offline-to-Online Link: Experiments demonstrate a monotonic relationship between the offline censoring-aware validation loss and online cumulative regret. Better offline predictive quality leads to lower online regret, confirming the theoretical deployment penalty bound.
Robustness to Mismatch:
- Distribution Shift: When tested on a Weibull environment after being pretrained on a mixture of four different demand families, ChronosFlow-ICGPS significantly outperforms misspecified parametric TS, showing robustness to family shifts.
- Prior Mismatch: In scenarios where the online test parameters lie outside the offline training regime, ChronosFlow-ICGPS remains stable, whereas parametric TS with a mismatched prior suffers high regret.
Real-World Benchmark (SuperStore Dataset): Using the SuperStore sales dataset (Hssaine & Sinclair, 2024), the method is evaluated under varying degrees of censoring severity ( $\lambda$ $λ$ ).
- Heavy Censoring: The "Meta" variant (pretrained on other datasets) achieves the largest gains in heavily censored regimes (e.g., $\lambda=1$ ), outperforming baselines like Sample Average Approximation (SAA), Kaplan-Meier, and RCN by a significant margin.
- Light Censoring: As censoring relaxes, the performance gap narrows, but the method remains competitive.

Significance and Claims

The paper claims to offer a novel template for solving sequential decision problems with decision-dependent uncertainty and continuous action spaces. Its primary significance lies in:

Unifying Framework: It successfully combines the strengths of parametric Bayesian methods (exploration via posterior sampling) and data-driven offline learning (robustness via meta-training) without requiring online gradient updates.
Theoretical Novelty: It provides the first sublinear Bayesian regret bound for Thompson Sampling in the censored newsvendor problem by reducing it to bandit convex optimization.
Practical Viability: The ChronosFlow architecture demonstrates that modern generative models (Transformers + Normalizing Flows) can be adapted to respect hard constraints (censoring) and perform effective in-context learning for operational problems.
Offline-to-Online Transfer: The work provides theoretical conditions under which offline predictive quality guarantees online decision performance, addressing a critical gap in data-driven operations research.

The authors position this work as a step toward "prediction-centric" decision-making, where the focus shifts from estimating parameters to generating consistent completions of latent trajectories to drive optimal actions.