No-Regret Learning in Bilateral Trade with Global Budget Balance

Core Concepts

Introducing global budget balance in bilateral trade algorithms enables the development of no-regret learning algorithms for adversarial scenarios.

Abstract

The content discusses the challenges and solutions in developing no-regret algorithms for bilateral trade under adversarial conditions. It introduces the concept of global budget balance and presents a two-phase algorithm to address the complexities of profit maximization and gain from trade. The content covers different feedback models, the importance of discretizing price spaces, and the comparison of results with prior research. Key insights include the impact of action space, partial feedback challenges, and the trade-off between profit and gain from trade.

Stats

In the full feedback model, the learner can guarantee ˜ 𝑂(√ 𝑇) regret against the best fixed prices in hindsight. A learning algorithm guarantees a ˜ 𝑂(𝑇 3/4) regret upper bound with one-bit feedback. The lower bound of Ω(𝑇 5/7) holds even in the two-bit feedback model.

Quotes

"The learner can guarantee ˜ 𝑂(√ 𝑇) regret against the best fixed prices in hindsight." "A learning algorithm guarantees a ˜ 𝑂(𝑇 3/4) regret upper bound with one-bit feedback." "The lower bound of Ω(𝑇 5/7) holds even in the two-bit feedback model."

Key Insights Distilled From

No-Regret Learning in Bilateral Trade via Global Budget Balance

by Martino Bern... at arxiv.org 03-28-2024

https://arxiv.org/pdf/2310.12370.pdf

Deeper Inquiries

How does the introduction of global budget balance impact the efficiency of bilateral trade algorithms

The introduction of global budget balance in bilateral trade algorithms has a significant impact on their efficiency. By relaxing the constraint of enforcing budget balance at each time step and instead requiring it to hold over the entire time horizon, algorithms can make more strategic pricing decisions. This flexibility allows the learner to reinvest profits gained in previous rounds, leading to a more optimal allocation of prices. Global budget balance enables algorithms to balance the trade-off between maximizing gain from trade and accumulating enough profit to maintain budget balance, resulting in more efficient outcomes in the long run.

What are the implications of the lower bound of Ω(𝑇 5/7) in the two-bit feedback model

The lower bound of Ω(𝑇 5/7) in the two-bit feedback model has important implications for the learnability of bilateral trade algorithms. This lower bound signifies the inherent complexity of the problem in this feedback setting, indicating that achieving sublinear regret is particularly challenging. The Ω(𝑇 5/7) lower bound sets a benchmark for the performance of algorithms in the two-bit feedback model, highlighting the difficulty of designing algorithms that can effectively learn and adapt to the adversarial nature of the bilateral trade environment with limited feedback.

How can the concept of global budget balance be applied to other economic scenarios beyond bilateral trade

The concept of global budget balance in bilateral trade can be applied to other economic scenarios beyond bilateral trade to enhance the efficiency and fairness of mechanisms. For example, in online marketplace platforms, global budget balance can ensure that pricing strategies are sustainable and do not lead to long-term losses for the platform. By enforcing global budget balance, platforms can optimize their pricing decisions over time, balancing the trade-off between maximizing revenue and maintaining financial stability. This concept can also be extended to various auction mechanisms, pricing strategies, and resource allocation problems in economic settings to improve overall outcomes and ensure economic viability.