Decision-Focused Forecasting: A Differentiable Multistage Optimisation Architecture

TL;DR

This work addresses continual multistage decision problems where forecasts influence future decisions. It introduces Decision-Focused Forecasting (DFF), a differentiable recurrent architecture that unrolls multistage optimisation with a planning horizon $h$ and propagates gradients across stages to capture intertemporal effects. The authors derive and analyze a state-path gradient adjustment and intertemporal gradient via KKT differentiations to align forecast models with downstream decisions, demonstrating improvements over single-stage DFL and two-stage baselines in energy storage arbitrage and portfolio optimisation. While showing promise, the approach incurs substantial training cost and presents stability challenges, motivating future work on stability enhancements, multi-scenario extensions, and faster differentiable optimisation techniques.

Abstract

Most decision-focused learning work has focused on single stage problems whereas many real-world decision problems are more appropriately modelled using multistage optimisation. In multistage problems contextual information is revealed over time, decisions have to be taken sequentially, and decisions now have an intertemporal effect on future decisions. Decision-focused forecasting is a recurrent differentiable optimisation architecture that expresses a fully differentiable multistage optimisation approach. This architecture enables us to account for the intertemporal decision effects of forecasts. We show what gradient adjustments are made to account for the state-path caused by forecasting. We apply the model to multistage problems in energy storage arbitrage and portfolio optimisation and report that our model outperforms existing approaches.

Figures (4)

• Figure 1: DFF: A deterministic policy approach expressed as a recurrent neural architecture.
• Figure 2: Development of test losses over training on the battery storage arbitrage task. 2-sigma error bars from five training runs. 2S denotes a two stage approach. The M refers to multistage optimisation, the S refers to single-stage optimisation. DFF was trained for 8 epochs, the other two for 50 to balance the relative intensity of computation.
• Figure 3: Forecasts produced by the tested model for the battery storage task following one of the experiments. For DFF we also plot the forecasts for contexts $i$ stages after the original one to demonstrate the relative stability of the representation, a phenomenon not shared with other models.
• Figure 4: Development of test losses over training on the portfolio optimisation task. 2-sigma error bars from $15$ training runs. $1/N$ denotes the performance of a portfolio with equal weights.