Online Search with Predictions: Pareto-optimal Algorithm and its Applications in Energy Markets

TL;DR

This work studies learning-augmented online decision-making for energy trading under price volatility by integrating ML predictions into online $k$-search. It develops Pareto-optimal threshold-based algorithms that simultaneously achieve high consistency when predictions are accurate and robust worst-case guarantees for arbitrary errors, framed via the consistency-robustness trade-off. The approach extends from basic online search to inventory-enabled OSID, preserving Pareto-optimality under large inventory and validating performance on real energy-market traces. The results demonstrate improved average performance and stronger worst-case behavior, highlighting the practical impact on storage-assisted energy procurement and related online trading problems. Overall, the paper provides a principled, theoretically grounded methodology for leveraging predictions in online energy trading with provable guarantees and practical relevance.

Abstract

This paper develops learning-augmented algorithms for energy trading in volatile electricity markets. The basic problem is to sell (or buy) $k$ units of energy for the highest revenue (lowest cost) over uncertain time-varying prices, which can framed as a classic online search problem in the literature of competitive analysis. State-of-the-art algorithms assume no knowledge about future market prices when they make trading decisions in each time slot, and aim for guaranteeing the performance for the worst-case price sequence. In practice, however, predictions about future prices become commonly available by leveraging machine learning. This paper aims to incorporate machine-learned predictions to design competitive algorithms for online search problems. An important property of our algorithms is that they achieve performances competitive with the offline algorithm in hindsight when the predictions are accurate (i.e., consistency) and also provide worst-case guarantees when the predictions are arbitrarily wrong (i.e., robustness). The proposed algorithms achieve the Pareto-optimal trade-off between consistency and robustness, where no other algorithms for online search can improve on the consistency for a given robustness. Further, we extend the basic online search problem to a more general inventory management setting that can capture storage-assisted energy trading in electricity markets. In empirical evaluations using traces from real-world applications, our learning-augmented algorithms improve the average empirical performance compared to benchmark algorithms, while also providing improved worst-case performance.

Figures (8)

• Figure 1: Illustrating Pareto-optimal boundaries of $k$-max search and $k$-min search. All curves start from a point $(\alpha^{(k)}_*,\alpha^{(k)}_*)$ (or $(\varphi^{(k)}_*,\varphi^{(k)})_*$) with both consistency and robustness equal to the corresponding worst-case optimal competitive ratio (CR), and end at the point $(\theta,1)$. We set $p_{\text{max}} = 50$, $p_{\text{min}} = 5$ and $\theta = p_{\text{max}}/p_{\text{min}} = 10$, where $p_{\text{max}}$ and $p_{\text{min}}$ are upper and lower bounds of prices over the time horizon.
• Figure 2: Comparing consistency-robustness trade-offs of baseline algorithms and Pareto-optimal algorithms for $k$-max and $k$-min search. $p_{\text{max}} = 50$ and $p_{\text{min}} = 5$.
• Figure 3: Threshold values for $k$-max search with $p_{\text{max}} = 50$, $p_{\text{min}} = 5$, $k = 20$, $\eta = 1.52$, and $\gamma = 2.63$.
• Figure 4: Cost ratio vs. different problem parameters. Dallas Jan 2023 with half-hour prediction window.
• Figure 5: Comparing algorithms for $k$-max search.

Theorems & Definitions (20)

• Lemma 2.1: $k$-max search
• Lemma 2.2: $k$-min search
• Lemma 2.3
• Theorem 3.1
• Definition 3.2: $p$-instance
• Theorem 3.3
• Proposition 3.4
• Proposition 3.5
• Theorem 3.6
• Theorem 3.7