Learning-Augmented Online Bidding in Stochastic Settings

TL;DR

The paper addresses online bidding under stochastic information by studying distributional predictions and randomized algorithms. It introduces an LP-based approach to compute Pareto-optimal bidding strategies that trade off consistency and robustness, and shows how to extend partial, finite strategies to full infinite strategies. It also analyzes randomized bidding, providing upper and lower bounds that reveal when randomness offers real benefits and when its advantage vanishes as the robustness requirement grows. The methodology further extends to dynamic predictions and related problems like contract scheduling and linear search, with experimental results confirming practical gains over naive heuristics.

Abstract

Online bidding is a classic optimization problem, with several applications in online decision-making, the design of interruptible systems, and the analysis of approximation algorithms. In this work, we study online bidding under learning-augmented settings that incorporate stochasticity, in either the prediction oracle or the algorithm itself. In the first part, we study bidding under distributional predictions, and find Pareto-optimal algorithms that offer the best-possible tradeoff between the consistency and the robustness of the algorithm. In the second part, we study the power and limitations of randomized bidding algorithms, by presenting upper and lower bounds on the consistency/robustness tradeoffs. Previous works focused predominantly on oracles that do not leverage stochastic information on the quality of the prediction, and deterministic algorithms.

Figures (5)

• Figure 1: Comparison between the deterministic tight upper bound on the consistency, and the randomized upper and lower bound of Theorems \ref{['thm:randomized.performance']} and \ref{['thm:final.randomized.bound']}.
• Figure 2: Empirical consistency as a function of the robustness requirement $r$.
• Figure 3: Empirical consistency when $\mu$ is comprised of two equiprobable points, with $\mu_1=5000$ and $\mu_2$ generated as specified in the caption. (a) is adversarial for $\rho=r/2$ and (b) for $\rho=\zeta_2$.
• Figure 4: Empirical consistency as a function of the robustness requirement $r$, where $\mu_i$ and $p_i$ are drawn i.i.d. following uniform distributions. Fig.(a) depicts the same values as (b), but has a wider $y$-axis so as to illustrate the relative performance of the heuristic with base $\zeta_1$.
• Figure 5: Empirical consistency as a function of the robustness requirement $r$, when $p_i$ are equal, and the $\mu_i$ are drawn from the stated distributions.

Theorems & Definitions (31)

• Definition 1
• Proposition 2
• Definition 3
• Definition 4
• Lemma 5
• Lemma 6
• Theorem 7
• Theorem 8
• Proposition 9
• Theorem 10