3. Use a model ladder with clear promotion conditions

Model-selection decision tree

Choose a demand estimator first; a separate constrained optimiser picks among approved prices. “Logs ready?” means usable demand, price exposure, cost and inventory histories. “Effect + support?” needs defensible identification and observations near the candidate prices, not a good forecasting score. For identified, uncensored demand, fit the GLM baseline before judging whether its remaining errors justify a more flexible challenger.

1. Check data, evidence and inventory readiness

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flowchart TB
    accTitle: Check readiness for price-response modeling
    accDescr: Repair missing logs, retain forecasting when causal support is absent, and separate inventory extensions before continuing to the GLM baseline.
    R{"Logs<br/>ready?"}
    I{"Effect +<br/>support?"}
    S{"Stock<br/>issues?"}
    A["A<br/>Repair<br/>logs"]
    B["B<br/>Forecast<br/>only"]
    C["C<br/>Inventory<br/>extension"]
    G["Fit GLM<br/>Next tree"]

    R -->|No| A
    R -->|Yes| I
    I -->|Yes| S
    I -->|No| B
    S -->|Yes| C
    S -->|No| G

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    classDef decision fill:#FFF5DF,stroke:#A8751A,color:#17324D,stroke-width:1.5px
    classDef execution fill:#E9F6F2,stroke:#23866E,color:#17324D,stroke-width:1.5px
    classDef neutral fill:#F5F7FA,stroke:#8796A8,color:#17324D,stroke-width:1.5px
    class R,I,S decision
    class A data
    class B neutral
    class C,G model

The letters link each outcome to its requirements below. “Stock issues?” covers sales censored by stockouts and decisions tied to future inventory or replenishment, which need a separate extension. Having a model does not authorise a new price, and more rows cannot repair missing identification or price support. The “Fit GLM” path continues in the promotion tree below.

2. Decide whether the GLM needs a challenger

Follow this tree after the readiness checks above. Fit the GLM first, then use forward error analysis to decide whether a boosted comparison is worth running. Choosing a challenger does not show it beats the baseline.

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flowchart TB
    accTitle: Compare a boosted demand challenger with the GLM
    accDescr: Retain the interpretable GLM unless nonlinear errors justify comparing a boosted demand challenger on forward validation.
    G["Fit log-price GLM"]
    N{"GLM errors<br/>nonlinear?"}
    D["D<br/>Keep GLM"]
    E["E<br/>Boosted<br/>challenger"]

    G --> N
    N -->|No| D
    N -->|Yes| E

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    classDef neutral fill:#F5F7FA,stroke:#8796A8,color:#17324D,stroke-width:1.5px
    class G,D,E model
    class N decision

• A · Repair the logs; keep the current approved policy. Model: no new price-response model yet. Missing exposures, costs or inventory make the decision target unreliable. Required: posted prices, exposed opportunities including non-purchases, timestamped costs and stock/availability. Proceed when reconciliation and readiness checks pass, and forecast only what the records support. See the data contract.
• B · Forecast only; gather intervention evidence. Model: a seasonal/count demand forecast, keeping the current approved pricing policy. Forecasting history cannot identify demand under a price change. Required for promotion: a bounded, approved price experiment or another defensible identification design, with local support for the proposed grid. Promote only within that identified, supported price region. See price-effect identification and the experiment design.
• C · Add a censored-demand/inventory extension only when supported. Model: a justified latent-demand distribution, with censor-aware estimation when sales are censored, plus a separate inventory optimisation model when decisions interact over time. Realised sales alone cannot reveal demand above available stock. Required: stock and availability histories, exposure, price/cost state, identifiable price effects and a validated observation/censoring model. Dynamic decisions also need replenishment and transition evidence. Promote after validating the observation model and demand-distribution calibration under the inventory rules; otherwise abstain from the unsupported price change. See the stock-censored research and simulator extension.
• D · Start with a regularised log-price Poisson or negative-binomial GLM. It gives an interpretable count-demand baseline, handles zero counts and can model exposure explicitly. Required: repeated product-market observations, valid exposure denominators, uncensored demand for this baseline, credible supported price variation and documented identification assumptions. Check forward performance, dispersion and uncertainty. See the elasticity baseline.
• E · Compare CatBoost or LightGBM with that GLM. Rich features and nonlinear seasonal/product interactions can justify a flexible demand challenger. Required: the same identified price evidence and support, features available at decision time, and a held-out forward comparison of accuracy, calibration, response curves and operating cost. Keep the GLM if the challenger adds nothing useful. See the boosted demand challenger.

Only a supported demand response moves on to the constrained price policy. There, feasibility, predictive risk and selection-adjusted improvement gate every candidate before selection. This tree organises the existing project work. Inventory and other advanced extensions stay outside its 25-hour practice budget.

These promotion gates are engineering recommendations. Model documentation sets out supported losses and estimator assumptions, not which model wins on your data.

The elasticity baseline

For counts, fit the conditional mean instead of taking the log of observed zero sales:

log E[units | p, x] = log(exposure)
                     + item_effect + store_effect + calendar_effect
                     + beta × log(p) + other_pre_decision_features

Here beta is the elasticity of the conditional mean: a 1% price increase goes with roughly a beta% change in demand, holding the modelled features fixed. An estimate of -1.4 suggests about a 1.4% decrease. It is a causal elasticity only under the identification assumptions in the next section.

A Poisson log-link handles zero counts naturally. Check for overdispersion (variance above the mean); a negative-binomial model may fit it better. Use partial pooling or regularisation when many products have little price variation. If you fit log-log regression on positive sales instead, state that zeros are excluded and handle retransformation bias. log1p(units) loses the usual elasticity meaning. statsmodels documents the GLM families and links.

Check how your implementation handles dispersion. In statsmodels' negative-binomial GLM family, you supply alpha; choosing the family does not estimate it. Estimate or tune dispersion on training data with a suitable count model, then check the tails on held-out data. The family documentation states this contract.

The boosted demand challenger

CatBoost is a useful challenger when product, store and category identifiers matter most. LightGBM suits larger tabular panels. Both support Poisson and quantile objectives, as the CatBoost loss documentation and LightGBM parameters show. Choose by careful validation and operating needs, not a generic leaderboard.

Use a count loss for units. For zero-heavy, nonnegative continuous spending, compare a Tweedie or two-part model where suitable. A hurdle model can separate whether someone buys from how many units, but the extra complexity needs validation. Keep the response scale explicit: a library may return a raw log score or a transformed mean, depending on prediction settings.

Inspect demand curves across the supported price grid in real customer-market contexts. A monotonic constraint (demand falls as price rises) can encode a reasonable own-price assumption, but it cannot fix confounding. Check that your objective supports that constraint in the pinned library version. Flexible trees extrapolate poorly beyond observed prices, and a smooth curve does not prove a price change will work.

A boosted Poisson-loss model estimates a conditional mean. That objective alone does not validate a Poisson demand distribution, and a few fitted quantiles are not a complete distribution either. For inventory or downside-risk calculations, supply a coherent nonnegative demand distribution or a justified tail estimator, and validate dispersion, tail calibration and interval ordering. Keep uncertainty in the fitted mean separate from future demand variation.

When advanced models earn their place

For strong substitutes, estimate category demand and the no-purchase outside option, instead of maximising each SKU's apparent profit separately. A choice model's assumptions and feasibility matter as much as its fit. Personalised individual pricing is a separate product-policy decision that a pooled product-market demand model does not need.

Use a bandit only when exploration has been approved for the defined market and price grid. Start with a randomised fixed-grid experiment. Later, a contextual bandit can give more exposure to promising allowed prices while still exploring. Log the chosen action's real probability after all filters, inventory checks and policy constraints. The Vowpal Wabbit tutorial explains the context/action/reward/probability contract. A bandit optimising immediate purchases can lose money after discounts, returns or longer-term effects, so define a matured contribution reward.

Delayed feedback changes the learning contract. Declare a fixed return/settlement horizon and an allowance for late data. Keep recent decisions pending instead of giving them zero reward or updating only on quick outcomes. A whole decision cohort matures under one rule, and its reward may still miss later returns, so state that limit. Delays or missing outcomes can depend on price and reward. The peer-reviewed ICML study of unrestricted delay distributions separates reward-independent from reward-dependent delays, and ordinary bandit updates are not automatically valid in both. Start with scheduled updates on mature cohorts and an incumbent fallback. More elaborate delay-aware learning is an optional extension.

For a faster purchase or revenue proxy, individual-level correlation with settled profit is not enough. Check, with uncertainty, whether the randomised price effects on the proxy point the same way as those on matured contribution. The August 2026 delayed-feedback workshop paper by Lee and colleagues examines reward alignment and learning efficiency separately. Its marketplace example is underpowered, later overall lift is null and positive subgroup findings are exploratory, so it does not validate a retail pricing reward. Compare against an approved fixed-price policy, and confirm any proxy-driven policy with experimental settled-profit outcomes.

Optional depth: what the 2026 research adds

E[min(D, I) | price, context] = sum from q=1 to I of P(D >= q | price, context)