Title: Online Bilateral Trade With Minimal Feedback: Don’t Waste Seller’s Time
Venue: NeurIPS 2025
Accepted: yes
Keywords: Bilateral Trade

Online Learning

Censored Feedback
Abstract: Online learning algorithms for designing optimal bilateral trade mechanisms have recently received significant attention. This paper addresses a key inefficiency in prior two-bit feedback models, which synchronously query both the buyer and the seller for their willingness to trade. This approach is inherently inefficient as it offers a trade to the seller even if the buyer rejects the offer. We propose an asynchronous mechanism that queries the seller only if the buyer has already accepted the offer. Consequently, the mechanism receives one bit of feedback from the buyer and a "censored" bit from the seller---a signal richer than the standard one-bit (trade/no-trade) feedback, but less informative than the two-bit model. Assuming independent valuations with bounded densities---the same distributional conditions underlying the two-bit results of Cesa-Bianchi et al. [2024a]---we design an algorithm that achieves $\tilde{O}(T^{2/3})$ regret against the best fixed price in hindsight. This matches the lower bound for the strictly richer two-bit model, showing that our mechanism elicits the minimal feedback necessary to attain optimal rates.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nBilateral trading refers to the situation in which a buyer and a seller wish to trade an asset through an intermediary. The goal of the intermediary is to post a price that maximizes gains from trade (or, equivalently, total welfare). In an online learning setting, the price is chosen dynamically based on the feedback received by the intermediary at the end of each trading round. In the one-bit model, the intermediary only observes whether the trade has occurred or not. However, it is known that this is insufficient for learning optimal price-setting strategies. In the two-bit model, the intermediary simultaneously observes whether the buyer and the seller are willing to trade. In this case, it is known that the bound on the regret is O(T^{2/3}). The contribution of this paper is to show that the same bound can be achieved under weaker feedback (3/2-bit, roughly speaking). The paper presents an algorithm where the seller is queried only after the buyer accepts the trade, effectively minimizing the amount of information that the intermediary has to collect from the seller while still achieving an optimal regret rate.\n\nSTRENGTHS AND WEAKNESSES:\nThe problem formulation is precise. The paper is well-written, and it has been a pleasure to read. Although the work is strongly based Cesa-Bianchi et al. [2024a] and incremental, the extension to asynchronous interaction is new to the best of my knowledge. The result of achieving an optimal regret rate with minimal feedback is strong.\n\nQUESTIONS:\nI understand that the focus here is on minimizing feedback from the seller for obvious practical reasons (lines 52-61). However, it seems to me that the roles of the buyer and the seller are theoretically interchangeable in your setup. Therefore, I'm left with the question of whether, theoretically, your algorithm can be easily adopted in a scenario where we want to minimize the feedback from the buyer (i.e., query the buyer only after the seller accepts the trade). In this case, I recommend briefly mentioning it somewhere in the paper, dropping \"Don't Waste Seller's Time\" from the title, and keeping only \"Online Bilateral Trade With Minimal Feedback\" for clarity.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-04"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose an asynchronous protocol for the online bilateral trade problem, designed to be more efficient by not wasting a seller's time. The proposed asynchronous mechanism queries the buyer and only approaches the seller if the buyer agrees to the price. The main contribution is an algorithm for this new setting that achieves a regret that matches the known lower bound.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n1. The paper's primary strength is the introduction of the \"Don't Waste Seller's Time\" asynchronous protocol. This is a more efficient model.\n\n2. The analysis presents a technical contribution in handling the \"censored\" seller feedback. The authors overcome the challenge of having potentially fewer samples for the seller's valuation by showing that when this occurs, the buyer's acceptance probability is also low. \n\nWeakness:\n1. I don't quite understand how the examples mentioned in the Introduction—such as online freelance marketplaces (Upwork, Fiverr), ride-sharing platforms (Uber, Lyft, Grab), and rental intermediaries (Airbnb)—correspond to the framework presented in this paper. Could you explain in more detail how the paper's algorithm would be applied in these domains? Based on my own user experience, these platforms appear to display the seller's price directly, which seems to be a complete mismatch with the framework presented in this paper, where a broker sets a single price for both parties.\n\n2. The technical novelty is not clear, as the framework and algorithmic approach of this paper heavily overlap with Section 5 of 'Bilateral Trade: A Regret Minimization Perspective' by Cesa-Bianchi et al. [2024a]. Even thought the authors argue that the samples from sellers are asynchronous and asymmetric, the core concepts are the same: the decomposition principle, the grid-based approach, and the strategy of first estimating the integral terms and then using a bandit-style method to explore and exploit the local terms. The amount of new content proposed in this paper is quite limited.\n\n3. This paper has no experiments at all, neither on synthetic nor on real-world data. Therefore, without experiments, it's unclear how the algorithm actually performs in practice or how it behaves with a limited amount of data.\n\nQUESTIONS:\nSee weakness.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies the problem of online bilateral trading in an asynchronous setting. There are three agents involved; the seller, the buyer and the broker. At each round $t$, the broker sets a price $p_t$ and the trade occurs if $S_t<p_t<B_t$. The problem has been studied under different feedback models, namely the full feedback, where the broker observes both buyer’s and seller’s valuation, the 2-bit model where the broker observes separately the boolean random variable $X_1 = p<B$ and $X_2= p>S$ and the 1-bit model where the broker only observes the ternary boolean $X = S<p<B$. They consider an asynchronous model in between 1-bit and 2-bit, where the broker only observes the boolean $X_2= p>S$ if the buyer first accepts the price $p_t$.\nThe authors give an online learning algorithm that operates over a uniform grid of size $K=\\lceil T^{1/3} \\rceil $.They prove that their online bilateral trading algorithm in the latter feedback setting that achieves regret of $O(T^{2/3})$.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n- The paper is well written and well organized.\n- The idea of exploring a feedback model between 1-bit and 2-bits is novel in such a setting. \n\n### Weaknesses \n- It would be valuable to discuss how sensitive the algorithm is to violations (e.g., if densities have unbounded spikes) and whether weaker smoothness conditions (e.g., Hölder) suffice.\n\nQUESTIONS:\nHave you considered studying information-accuracy tradeoffs such as:\n- How much mutual information about the optimal price does each feedback bit supply ?\n- What regret rates are achievable if you deliberately limit feedback to, say, one bit every other round, or to noisy bits?\n- How much “value” does each bit contribute toward narrowing down the optimal price?\n\nFraming the problem in an information-theoretic bandit lens, that is, bounding regret in terms of cumulative mutual information between observations and the optimal actio, would let you precisely quantify when and why extra seller signals cease to help.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies the online bilateral trading problem, where a market maker (“broker”) aims at facilitating trades between pairs of buyers and sellers (drawn i.i.d.) arriving over time $t=1,2,\\ldots, T$ with a price $p_t$ in the middle. The performance is measured by regret on the gain from trade against the best fixed price in hindsight. The authors introduced an asynchronous feedback protocol, where the broker always observes the buyer’s willing-to-trade $1[p_t\\leq B_t]$ but only observes a  feedback from the seller’s side $1[S_t\\leq p_t]$ if the buyer has accepted the price, thus formulating a 1.5-bit-feedback censored feedback model. In this paper, the authors propose an algorithm that achieves $\\tilde{O}(T^{2/3})$ regret, which is near-optimal even for the two-bit feedback problem setting. The algorithm applies a pure-exploration-then-UCB strategy.\n\nSTRENGTHS AND WEAKNESSES:\n### Strength:\n\nThis problem is novel and well-motivated as it is only necessary to ask the seller’s side when the buyer has approved the trading. The 1.5-bit feedback model (as sometimes 1 and sometimes 2) is more difficult than the previous two-bit feedback model, and it is non-trivial to achieve the same regret rate. Regarding the identical regret rate (in big O notation), it also justifies that the 1.5-bit model is not losing too much information from the two-bit model, which aligns with many existing literatures on pricing and trading with censored feedback. Besides, the algorithmic analysis is rigorous and sound, with assumptions, theorems and lemmas clearly stated. The paper is overall well written.\n\n### Weakness:\n\nI think the most concern raised from my side is the lack of numerical experiments. Although this work is theoretic-oriented and the theoretical results are contributive, I still think it is particularly necessary for this paper to have at least simulations. The reason is simple as I would like to know whether the feedback censoring effect on the seller’s side is harming the reward or affecting the regret in practice (although the regret rate is the same in big O notation). There are two possible results as I expect: (1) The cumulative reward of proposed algorithm decreases faster than the baseline oracle, leading to a larger regret on the 1.5-bit problem than the original two-bit problem. This means that the algorithm suffers more than the baseline oracle from the censoring effect. (2) The regret is even smaller than the two-bit case, indicating that the baseline oracle suffers more than the algorithm (or the player in general). While (1) could be more reasonable, I wonder if (2) indeed happens, then it might still not be a “Waste of Seller’s Time” to ask both sides simultaneously. Do you agree with that?\n\nBesides, there are some drawbacks from the modeling assumptions, e.g. the finite price set, the i.i.d. assumption, the bounded density, etc. Some of them are not well justified.\n\nQUESTIONS:\n### Questions:\n\nPlease see “weakness” above. Also, what is the computational complexity of the algorithm, particularly the $K$-dependence as you adopt the grid-based approach?\n\n### Suggestions:\n\nSome typos to fix: e.g. Line 138 (the equation): “sellers’s”.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}