Large Scale Forecasting & Pricing Optimization
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Algorithmic pricing: Forecasting and Pricing How to use differential programming together with large scale models to find optimal prices in e-commerce?
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Large Scale Forecasting & Pricing Optimization
- 1. LARGE SCALE FORECASTING & PRICING Tofigh Naghibi
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- 5. 5 Forecaster: Oracle of all possible futures Optimizer: Find the ONE optimal future action FORECASTING & PRICING Forecaster Optimizer
- 6. 6 Forecast sales per article/object per shop/market for a given time horizon per time unit. FORECASTING & PRICING OVERVIEW Optimal price for a Given objective function (Revenue / profit, customer satisfaction) Given constraints (min profit, max accepted loss, max over-stock) Given optimization time horizon Given compute budget Forecasting Pricing
- 8. 8 PRICING STRATEGIES Reward (Object function) value becomes clear immediately ⇒ ● Far future is irrelevant ● Prediction is much easier ● You even can use online optimizer ● Can be quickly tested Long time horizon Short time horizon Reward (Objective function) value is revealed very late ⇒ ● Many time steps are dependent ● Prediction is difficult ● You need a proper optimizer ● Needs long term A/B test
- 9. 9 PRICING STRATEGIES Long time horizon Short time horizon ● Model-based reinforcement learning ○ Learn market model from historic data, D ○ Learn action policy: 𝞹(d|S) ○ Deterministic: Pure optimization ○ Stochastic: Exploration ● Multi-arm bandit / Online learning ○ Learn online or from historic data ○ Select an action/price ○ Observe its effect and update
- 10. 10 ● Many articles ○ Not sensible to have a model per article ● Frequent price updates ○ Forecast + Optimization need to be efficient/fast ● Many shops/markets ○ They might have interactions FORECASTING AT SCALE: CHALLENGES
- 11. 11 ● Various stakeholders ○ Might need forecast at different aggregation level ○ Training samples are not independent anymore ● Long forecasting horizons ○ Put a lot of pressure both computationally and accuray-wise on the system ○ Hard to evaluate FORECASTING AT SCALE: CHALLENGES
- 12. 12 ● ARIMA/ Prophet: One demand forecast model per article ○ Model management is an issue ○ Remember: The learned model SHOULD be a function of price Demand = f(price) Bigger problem: In short time series, not many price changes exist. Thus, demand approximation as a function of price will be very noisy TRADITIONAL FORECASTING METHODS
- 13. 13 ● One model shared among all articles ● Shop model can be shared or not but, they SHOULD communicate ● Able to provide the gradient of your function with respect to price MODERN APPROACH
- 15. 15 ● Develop models in gradient descent based frameworks ○ pyTorch, Chainer, maxNet, TensorFlow,.... ○ Yes it is neural network ○ No not all the models need to be neural network based. DIFFERENTIAL PROGRAMMING
- 17. 17 REAL-WORLD EXAMPLE Sales model Return rate model
- 18. 18 REAL-WORLD EXAMPLE Sales model Return rate model Over stock Err. Min
- 19. 19 ● Models can communicate via gradient ● Requirement: All models should implement gradient calculation REAL-WORLD EXAMPLE
- 20. 20 ● Solving optimization is simple: Use gradient ascent/descent. Gradient of the models are given almost for free. REAL-WORLD EXAMPLE
- 23. 23 ● Replacement of LSTM ○ Extremely parallelizable: O(1) in terms of seq length ● Bunch of feed-forward networks, much easier to go against overfitting TRANSFORMER Attention Is All You Need Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, Illia Polosukhin
- 24. 24 ● Multi-head attention mechanism ○ Attention: Every time point finds its similarity with every other time point in the seq ○ First the seq projected to k different sub-spaces and then attention is applied ● No hidden-state. Encoded output seq has the same length as the input seq ● It encodes a set TRANSFORMER
- 25. 25 Infrastructure ● Low-Latency super duper data processing pipeline ● Multi-GPU training ● Sagemaker, Kubernetes, Databricks for large scale analysis ● One-click training data with new features generation
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