Agentic Advertising

    Reinforcement learning for bidding: a practical primer on pacing, auto-bidding and evaluation

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    Reinforcement learning for bidding treats a campaign's day as a sequence of decisions: each bid spends budget that later bids cannot use. Research since 2017 shows learned policies can beat fixed rules, and Alibaba reports production use. Most published production systems still pace with feedback controllers, so treat RL as a challenger you evaluate carefully.

    Contents

    Key facts

    • The framing dates from 2017. Cai et al. formulated real-time bidding as a Markov decision process whose state holds auction information and the campaign's live parameters, and whose action is the bid price (Cai et al., WSDM 2017, arXiv).
    • Alibaba reports RL in production. Zhao et al. "deployed the SS-RTB system in the e-commerce search auction platform of Alibaba" (Zhao et al., KDD 2018, arXiv). A later generative bidder raised GMV by 2.81% and ROI by 3.36% in an online A/B test there (Guo et al., KDD 2024, arXiv).
    • Simulators mislead. Mou et al. argued that gaps between a virtual advertising system and the real one cause "inconsistency between online and offline". They proposed training against the live system with safe exploration instead (Mou et al., NeurIPS 2022, arXiv).
    • There is now a public benchmark. AuctionNet ships an auction environment and a dataset of 10 million ad opportunities, 48 bidding agents and more than 500 million auction records (Su et al., arXiv, 14 December 2024).
    • Controllers still run pacing at scale. DoorDash's Smart Fast Finish, a rule-tuned pacing feature, is "currently in use at DoorDash" and was validated with budget-split experiments (Garg et al., arXiv, 9 September 2025).
    Jump to the table

    Definition

    Reinforcement learning (RL) for bidding: training a bidding policy that maps the current auction and campaign state to a bid or a bid multiplier. The goal is the campaign's total reward over a period, under budget and cost constraints. The policy learns from logged or live interaction rather than from labelled examples.

    Two problems share this name. Budget pacing decides how fast to spend. Auto-bidding decides how much each impression is worth bidding, given a goal such as conversions at a target cost. Many production systems split them; RL papers often solve both at once. Both run inside a demand-side platform (DSP) or an ad platform's own auction, as part of real-time bidding. This page sits in the agentic advertising hub. For the auction itself, see how real-time bidding works.

    Why bidding looks like a reinforcement learning problem

    A single bid looks like a prediction problem: estimate the impression's value, then bid. The budget changes that. Money spent in the morning is gone by evening, when the same audience might be cheaper. The bid landscape, the distribution of winning prices, also shifts hour by hour. Each bid changes the state the next bid faces, which is exactly the setting RL is built for.

    5 of 5 rows

    Columns (3)

    State

    What the bidder knows now

    Time left in the day, budget left, spend rate, recent win rate, recent cost per acquisition

    Action

    What the bidder controls

    A bid price per impression, or a multiplier λ applied to predicted value for the next interval

    Reward

    What the campaign wants

    Clicks or conversions won, value minus cost, penalties for missing a cost target

    Transition

    How the market reacts

    Competitors' bids, traffic volume and the auction's clearing prices

    Episode

    The planning horizon

    One day or one flight of a campaign

    State

    In bidding

    What the bidder knows now

    Example

    Time left in the day, budget left, spend rate, recent win rate, recent cost per acquisition

    Action

    In bidding

    What the bidder controls

    Example

    A bid price per impression, or a multiplier λ applied to predicted value for the next interval

    Reward

    In bidding

    What the campaign wants

    Example

    Clicks or conversions won, value minus cost, penalties for missing a cost target

    Transition

    In bidding

    How the market reacts

    Example

    Competitors' bids, traffic volume and the auction's clearing prices

    Episode

    In bidding

    The planning horizon

    Example

    One day or one flight of a campaign

    Download JSON

    Table by AdSovereign, CC BY 4.0.

    Most practical systems act on a multiplier every few minutes, not on every bid. Cai et al. note that the large real-world auction volume forced them to approximate state values with neural networks (Cai et al., WSDM 2017). Wu et al. found that the immediate reward "is misleading under a critical resource constraint". They designed a learned reward instead (Wu et al., CIKM 2018, arXiv).

    The baseline you must beat: pacing controllers and dual multipliers

    Before any RL, a bidder needs a baseline. The common one bids predicted value scaled by a multiplier and adjusts the multiplier with feedback. In a first-price auction the result is then shaded; in a second-price auction it can be bid as is. Theory supports this design: for budget-constrained bidding in repeated auctions, a dual-variable multiplier that learns from spend gives strong guarantees (Balseiro and Gur, Management Science, 2019). Aggarwal, Badanidiyuru and Mehta analysed autobidding under several constraints in the same spirit (WINE 2019).

    The loop below is the shape of such a controller. It is pseudo-code for illustration, not any platform's implementation.

    every interval (for example 5 minutes):
        target_spend   = budget_total * planned_share_of_day(elapsed)
        error          = (spend_so_far - target_spend) / budget_total
        lambda         = clamp(lambda + k * error, 0, lambda_max)   # spend too fast -> raise lambda
    for each bid request:
        value          = predicted_conversion_prob * value_per_conversion
        bid            = value / (1 + lambda)                       # pacing
        bid            = shade(bid, predicted_winning_price)        # first-price shading

    Published production work refines this loop rather than replacing it. A Google-authored field guide compares ways to combine budget pacing with return-on-spend pacing. It finds that taking the minimum of two separate multipliers performs almost as well as a fully coupled dual method (Balseiro et al., arXiv 2023, ICML 2024). A 2025 paper adds hysteresis to proportional feedback and reports 13% lower pacing error and 54% lower multiplier volatility in real auctions (Apparaju, Niu and Qi, arXiv, 29 September 2025).

    Some platforms describe the same tools in plain terms. Topsort's documentation lists two pacing mechanisms: throttling, which excludes a campaign from some auctions, and discount pacing, which lowers bids to slow spending (Topsort docs, accessed 9 November 2026). Smart Pacing, from Yahoo researchers, learned pacing rates from data and was implemented in a production DSP (Xu et al., KDD 2015, arXiv).

    An RL policy is worth deploying only if it beats a well-tuned version of this baseline on the same traffic. The shading step in the last line is covered in bid shading explained.

    Published RL approaches, in date order

    The table lists the papers most cited in this area, with authors, venue and what each one says about real deployment. "Deployment evidence" quotes the paper's own claim; none has been independently verified.

    9 of 9 rows

    Columns (5)

    2017

    Han Cai, Kan Ren, Weinan Zhang, Kleanthis Malialis, Jun Wang, Yong Yu, Defeng Guo

    Bidding as an MDP; neural value approximation for scale

    Experiments on real-world auction data

    2018

    Di Wu, Xiujun Chen, Xun Yang, Hao Wang, Qing Tan, Xiaoxun Zhang, Jian Xu, Kun Gai

    Learned reward design for constrained bidding

    "Easy to be deployed in large-scale industrial applications"

    2018

    Junqi Jin, Chengru Song, Han Li, Kun Gai, Jun Wang, Weinan Zhang

    Clustered advertisers, coordinated agents

    Industry-scale real data

    2018

    Jun Zhao, Guang Qiu, Ziyu Guan, Wei Zhao, Xiaofei He

    Robust MDP at hourly level; control-by-model

    Deployed in Alibaba's e-commerce search auction

    2021

    Yue He, Xiujun Chen, Di Wu, Junwei Pan, Qing Tan, Chuan Yu and others

    One framework for several constraint types (USCB)

    n/d in sources read

    2022

    Zhiyu Mou, Yusen Huo, Rongquan Bai, Mingzhou Xie, Chuan Yu, Jian Xu, Bo Zheng

    Train against the live system with safe exploration

    Simulated and real-world experiments

    2024

    Jiayan Guo, Yusen Huo, Zhilin Zhang, Tianyu Wang, Chuan Yu, Jian Xu, Yan Zhang, Bo Zheng

    Diffusion model generates whole bid trajectories

    Online A/B test at Alibaba: GMV +2.81%, ROI +3.36%

    2024

    AuctionNet, arXiv

    Kefan Su, Yusen Huo, Zhilin Zhang, Shuai Dou, Chuan Yu, Jian Xu, Zongqing Lu, Bo Zheng

    Public benchmark: environment, dataset, baselines

    Derived from a real advertising platform

    2025

    Zhiyu Mou, Miao Xu, Wei Chen, Rongquan Bai, Chuan Yu, Jian Xu

    Learn an environment model from real data, penalise model errors

    "Real-world experiments"

    2017

    Paper and venue

    RTB by RL in Display Advertising, WSDM

    Authors

    Han Cai, Kan Ren, Weinan Zhang, Kleanthis Malialis, Jun Wang, Yong Yu, Defeng Guo

    Idea

    Bidding as an MDP; neural value approximation for scale

    Deployment evidence (paper's claim)

    Experiments on real-world auction data

    2018

    Authors

    Di Wu, Xiujun Chen, Xun Yang, Hao Wang, Qing Tan, Xiaoxun Zhang, Jian Xu, Kun Gai

    Idea

    Learned reward design for constrained bidding

    Deployment evidence (paper's claim)

    "Easy to be deployed in large-scale industrial applications"

    2018

    Paper and venue

    RTB with Multi-Agent RL, CIKM

    Authors

    Junqi Jin, Chengru Song, Han Li, Kun Gai, Jun Wang, Weinan Zhang

    Idea

    Clustered advertisers, coordinated agents

    Deployment evidence (paper's claim)

    Industry-scale real data

    2018

    Authors

    Jun Zhao, Guang Qiu, Ziyu Guan, Wei Zhao, Xiaofei He

    Idea

    Robust MDP at hourly level; control-by-model

    Deployment evidence (paper's claim)

    Deployed in Alibaba's e-commerce search auction

    2021

    Authors

    Yue He, Xiujun Chen, Di Wu, Junwei Pan, Qing Tan, Chuan Yu and others

    Idea

    One framework for several constraint types (USCB)

    Deployment evidence (paper's claim)

    n/d in sources read

    2022

    Authors

    Zhiyu Mou, Yusen Huo, Rongquan Bai, Mingzhou Xie, Chuan Yu, Jian Xu, Bo Zheng

    Idea

    Train against the live system with safe exploration

    Deployment evidence (paper's claim)

    Simulated and real-world experiments

    2024

    Paper and venue

    AIGB: Generative Auto-bidding, KDD

    Authors

    Jiayan Guo, Yusen Huo, Zhilin Zhang, Tianyu Wang, Chuan Yu, Jian Xu, Yan Zhang, Bo Zheng

    Idea

    Diffusion model generates whole bid trajectories

    Deployment evidence (paper's claim)

    Online A/B test at Alibaba: GMV +2.81%, ROI +3.36%

    2024

    Paper and venue

    AuctionNet, arXiv

    Authors

    Kefan Su, Yusen Huo, Zhilin Zhang, Shuai Dou, Chuan Yu, Jian Xu, Zongqing Lu, Bo Zheng

    Idea

    Public benchmark: environment, dataset, baselines

    Deployment evidence (paper's claim)

    Derived from a real advertising platform

    2025

    Authors

    Zhiyu Mou, Miao Xu, Wei Chen, Rongquan Bai, Chuan Yu, Jian Xu

    Idea

    Learn an environment model from real data, penalise model errors

    Deployment evidence (paper's claim)

    "Real-world experiments"

    Download JSON

    Table by AdSovereign, CC BY 4.0.

    The pattern is clear. Most production evidence comes from one company, Alibaba, on its own closed auctions. That matters, because a platform that runs the auction sees every competitor's bid. An independent DSP bidding into other people's exchanges sees far less of the market.

    What runs in production, according to public sources

    Few ad platforms publish engineering detail on bidding. The table separates what is described as reinforcement learning from what is described as control or rules.

    5 of 5 rows

    Columns (4)

    Alibaba

    RL bidder deployed in e-commerce search auction; generative auto-bidder tested online

    Yes

    DoorDash

    Smart Fast Finish: adjusts start time and throttle rate from historical campaign data to stop overdelivery

    No, tuned control

    Google (paper authors)

    Budget and return-on-spend pacing algorithms compared on data from a large advertising platform

    No, dual-based pacing

    Topsort

    Throttling and discount pacing in its auction

    Not stated

    Yahoo (paper authors)

    Smart Pacing learned from data in a real DSP

    No, adaptive control

    Alibaba

    What the public source describes

    RL bidder deployed in e-commerce search auction; generative auto-bidder tested online

    RL?

    Yes

    DoorDash

    What the public source describes

    Smart Fast Finish: adjusts start time and throttle rate from historical campaign data to stop overdelivery

    RL?

    No, tuned control

    Google (paper authors)

    What the public source describes

    Budget and return-on-spend pacing algorithms compared on data from a large advertising platform

    RL?

    No, dual-based pacing

    Yahoo (paper authors)

    What the public source describes

    Smart Pacing learned from data in a real DSP

    RL?

    No, adaptive control

    Download JSON

    Table by AdSovereign, CC BY 4.0.

    Vendors that sell "AI bidding" rarely say which method they use. Ask whether the system learns a policy over time, or predicts value per impression and paces with a controller. Both are valid; they fail in different ways. How to question such a system is covered in explainable AI in bidding.

    Formulating the problem: an environment specification

    Write the environment down before choosing an algorithm. The specification below is our illustrative format. It fixes what the policy sees, what it controls, how it is scored and which limits it can never break.

    {
      "environment": "display_cpa_campaign_day",
      "episode": { "length_hours": 24, "decision_interval_minutes": 5, "steps": 288 },
      "state": [
        "fraction_of_day_elapsed",
        "fraction_of_budget_spent",
        "spend_rate_last_interval",
        "win_rate_last_interval",
        "avg_clearing_price_cpm_last_interval",
        "conversions_so_far",
        "cpa_so_far_vs_target"
      ],
      "action": { "type": "continuous", "name": "lambda_multiplier", "min": 0.0, "max": 4.0 },
      "bid_rule": "bid_cpm = predicted_value_cpm / (1 + lambda_multiplier)",
      "reward": {
        "per_step": "conversions_won",
        "terminal_penalty": "max(0, cpa_achieved - cpa_target) * penalty_weight",
        "penalty_weight": 50
      },
      "hard_limits": {
        "max_bid_cpm_usd": 40.0,
        "max_spend_per_interval_share": 0.02,
        "budget_overspend_tolerance": 0.01
      },
      "baseline_policy": "proportional_pacing_controller_v3"
    }

    6 of 6 rows

    Columns (2)

    decision_interval_minutes

    Acting every 5 minutes, not every bid, keeps the policy cheap and the data dense

    state

    Only signals available at bid time; anything else leaks the future into training

    action

    A multiplier keeps the value model and the policy separate, so each can be checked

    reward.terminal_penalty

    Encodes the cost target; without it the policy simply spends the budget

    hard_limits

    Enforced outside the policy, so a bad model cannot break them

    baseline_policy

    The controller the RL policy must beat on the same traffic

    decision_interval_minutes

    Why it matters

    Acting every 5 minutes, not every bid, keeps the policy cheap and the data dense

    state

    Why it matters

    Only signals available at bid time; anything else leaks the future into training

    action

    Why it matters

    A multiplier keeps the value model and the policy separate, so each can be checked

    reward.terminal_penalty

    Why it matters

    Encodes the cost target; without it the policy simply spends the budget

    hard_limits

    Why it matters

    Enforced outside the policy, so a bad model cannot break them

    baseline_policy

    Why it matters

    The controller the RL policy must beat on the same traffic

    Download JSON

    Table by AdSovereign, CC BY 4.0.

    The hard_limits block is the most important part. Guardrails live in the bidder, not in the model, as described in RTB bidder architecture.

    Training: simulators, offline data and the sim-to-real gap

    RL needs interaction, and interaction costs money. Teams therefore train on simulators or on logged data first. Both have known failure modes.

    A simulator replays historical auctions and models competitors' responses. Mou et al. showed that gaps between such a virtual system and the real one make offline training unreliable. They proposed bounded, safe exploration in the live system instead (NeurIPS 2022). A 2025 paper from the same group describes the field moving from simulator-based RL to offline RL on fixed real datasets, then to learned environment models. It notes that offline policies are "limited by the dataset's state space coverage" (Mou et al., arXiv, 22 June 2025).

    The practical consequence for a DSP is simple. Your logs contain only the bids your current policy made. A new policy that bids very differently is asking about situations the logs never saw. Keep candidate policies close to the logged one at first, and widen the range as live data accumulates. Logs with full bid and price detail are the raw material; their structure is covered in log-level data.

    Evaluation: offline estimates, budget-split tests and guardrails

    A learned bidder should pass four gates, in order. Each gate is cheaper than the next and catches different failures.

    1. Offline replay. Estimate the new policy's results on logged data. Li et al.'s replay method gives unbiased estimates when the logging policy explored at random (Li et al., WSDM 2011, arXiv). Bidding logs rarely meet that condition, so treat replay results as optimistic.
    2. Benchmark environment. Compare against baselines on a shared environment such as AuctionNet, which includes linear programming, RL and generative baselines (Su et al., 2024).
    3. Budget-split online test. Ordinary A/B tests are biased in auctions, because treatment and control campaigns compete for the same impressions. Splitting each campaign's budget between arms removes that bias. Liu, Mao and Kang show the design is unbiased wherever buyers have a defined budget (Liu, Mao and Kang, arXiv, 16 December 2020). DoorDash used budget-split experiments to validate its pacing change (Garg et al., 2025).
    4. Staged rollout with guardrails. Move a small share of campaigns, with hard bid and spend caps, an automatic fallback to the baseline and a daily review of overspend and cost per acquisition.

    Risks and how to contain them

    6 of 6 rows

    Columns (3)

    Non-stationary market

    A policy trained on last month's prices misjudges today's

    Short retraining cycles; drift alerts on clearing prices

    Reward misspecification

    The policy hits the metric and misses the goal, for example cheap conversions of low value

    Reward reviewed by the business owner; secondary metrics in every test

    Interaction between bidders

    Many learning bidders in one auction can behave in unexpected ways; see Paes Leme et al., "Complex Dynamics in Autobidding Systems" (EC 2024)

    Damped updates; caps on how fast the multiplier can move

    Overspend

    The policy spends ahead of plan on a traffic spike

    Hard per-interval spend caps outside the model

    Opaque decisions

    Nobody can say why spend shifted

    Log state, action and reward per interval; see explainable AI in bidding

    Distribution shift in training data

    Offline data covers only past behaviour

    Conservative updates; staged exploration

    Non-stationary market

    What happens

    A policy trained on last month's prices misjudges today's

    Containment

    Short retraining cycles; drift alerts on clearing prices

    Reward misspecification

    What happens

    The policy hits the metric and misses the goal, for example cheap conversions of low value

    Containment

    Reward reviewed by the business owner; secondary metrics in every test

    Interaction between bidders

    What happens

    Many learning bidders in one auction can behave in unexpected ways; see Paes Leme et al., "Complex Dynamics in Autobidding Systems" (EC 2024)

    Containment

    Damped updates; caps on how fast the multiplier can move

    Overspend

    What happens

    The policy spends ahead of plan on a traffic spike

    Containment

    Hard per-interval spend caps outside the model

    Opaque decisions

    What happens

    Nobody can say why spend shifted

    Containment

    Log state, action and reward per interval; see explainable AI in bidding

    Distribution shift in training data

    What happens

    Offline data covers only past behaviour

    Containment

    Conservative updates; staged exploration

    Download JSON

    Table by AdSovereign, CC BY 4.0.

    The interaction risk is specific to auctions. When most buyers use learning bidders, each one's environment is the others' policies. A bidder that tests well alone can behave differently once rivals adapt to it. To see how inputs move a single bid, try the explainable AI RTB simulator.

    Common mistakes

    1. Skipping the baseline. Without a tuned controller on the same traffic, an RL gain cannot be measured.
    2. Plain A/B tests in an auction. Treatment and control compete for the same impressions; use budget-split designs.
    3. Letting the model own the limits. Bid caps and spend caps belong in the bidder, outside any learned component.
    4. Training on features not available at bid time. Leaked future data makes offline results look far better than live ones.
    5. Rewarding only volume. A reward without a cost term teaches the policy to spend the budget.
    6. Trusting replay estimates from non-random logs. Logged bids reflect the old policy; estimates far from it are guesses.
    7. Retraining without a changelog. If a policy changes weekly, record each version so audits can match bids to policies.

    FAQ

    What is reinforcement learning in bidding?
    It is a way to train a bidding policy that chooses bids or bid multipliers from the current state of the campaign and the market. The aim is the best result over a whole day or flight, not on each bid. The framing treats the budget as a resource that each bid uses up. Cai et al. set it out as a Markov decision process in 2017 (WSDM 2017).
    Do DSPs use reinforcement learning in production?
    Alibaba has published RL bidders deployed or tested online in its own auctions (Zhao et al., 2018; Guo et al., 2024). Most other public production accounts describe feedback controllers and dual multipliers for pacing. Independent DSPs rarely disclose which method their "AI bidding" uses.
    What is the difference between budget pacing and auto-bidding?
    Budget pacing controls how fast a fixed budget is spent through the day. Auto-bidding decides what each impression is worth bidding, given a goal such as a target cost per acquisition or return on ad spend (ROAS). Many platforms run them as separate systems; a Google-authored field guide compares ways to combine them (Balseiro et al., 2023).
    How do you test a learned bidder safely?
    Run offline replay first, then a benchmark environment, then a budget-split online test, then a staged rollout with hard caps and automatic fallback. Budget-split designs avoid the bias of ordinary A/B tests in auctions (Liu, Mao and Kang, 2020).
    Do I need reinforcement learning to bid well?
    No. A good value model, a tuned pacing controller and sound bid shading cover most campaigns. RL becomes worth testing when budgets, constraints and traffic patterns are complex enough that a controller leaves measurable value behind.

    How this works on owned infrastructure

    Everything on this page depends on logs: the state the bidder saw, the multiplier it chose and what the auction returned, interval by interval. A learned policy cannot be trained, replayed or audited without them. With a hosted DSP, those logs and the policy itself stay with the vendor. AdSovereign's bidder, pacing service and event pipeline are designed to run in the buyer's own cloud account or data centre, so a data science team can train a challenger policy on its own logs. It can then run a budget-split test against the existing controller with caps enforced in the bidder. The architecture page shows where pacing sits, and a pilot can scope such a test.

    Sources

    1. Han Cai, Kan Ren, Weinan Zhang, Kleanthis Malialis, Jun Wang, Yong Yu and Defeng Guo, "Real-Time Bidding by Reinforcement Learning in Display Advertising" (arXiv, 10 January 2017; WSDM 2017). https://arxiv.org/abs/1701.02490
    2. Di Wu, Xiujun Chen, Xun Yang, Hao Wang, Qing Tan, Xiaoxun Zhang, Jian Xu and Kun Gai, "Budget Constrained Bidding by Model-free Reinforcement Learning in Display Advertising" (arXiv, 23 February 2018; CIKM 2018). https://arxiv.org/abs/1802.08365
    3. Junqi Jin, Chengru Song, Han Li, Kun Gai, Jun Wang and Weinan Zhang, "Real-Time Bidding with Multi-Agent Reinforcement Learning in Display Advertising" (arXiv, 27 February 2018; CIKM 2018). https://arxiv.org/abs/1802.09756
    4. Jun Zhao, Guang Qiu, Ziyu Guan, Wei Zhao and Xiaofei He, "Deep Reinforcement Learning for Sponsored Search Real-time Bidding" (arXiv, 1 March 2018; KDD 2018). https://arxiv.org/abs/1803.00259
    5. Yue He, Xiujun Chen, Di Wu, Junwei Pan, Qing Tan, Chuan Yu et al., "A Unified Solution to Constrained Bidding in Online Display Advertising" (KDD 2021, 14 August 2021). https://doi.org/10.1145/3447548.3467199
    6. Zhiyu Mou, Yusen Huo, Rongquan Bai, Mingzhou Xie, Chuan Yu, Jian Xu and Bo Zheng, "Sustainable Online Reinforcement Learning for Auto-bidding" (arXiv, 13 October 2022; NeurIPS 2022). https://arxiv.org/abs/2210.07006
    7. Jiayan Guo, Yusen Huo, Zhilin Zhang, Tianyu Wang, Chuan Yu, Jian Xu, Yan Zhang and Bo Zheng, "AIGB: Generative Auto-bidding via Conditional Diffusion Modeling" (arXiv, 25 May 2024; KDD 2024). https://arxiv.org/abs/2405.16141
    8. Kefan Su, Yusen Huo, Zhilin Zhang, Shuai Dou, Chuan Yu, Jian Xu, Zongqing Lu and Bo Zheng, "AuctionNet: A Novel Benchmark for Decision-Making in Large-Scale Games" (arXiv, 14 December 2024). https://arxiv.org/abs/2412.10798
    9. Zhiyu Mou, Miao Xu, Wei Chen, Rongquan Bai, Chuan Yu and Jian Xu, "Permutation Equivariant Model-based Offline Reinforcement Learning for Auto-bidding" (arXiv, 22 June 2025). https://arxiv.org/abs/2506.17919
    10. Jian Xu, Kuang-chih Lee, Wentong Li, Hang Qi and Quan Lu, "Smart Pacing for Effective Online Ad Campaign Optimization" (arXiv, 18 June 2015; KDD 2015). https://arxiv.org/abs/1506.05851
    More sources (9)
    1. Santiago R. Balseiro and Yonatan Gur, "Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium", Management Science (September 2019). https://doi.org/10.1287/mnsc.2018.3174
    2. Gagan Aggarwal, Ashwinkumar Badanidiyuru and Aranyak Mehta, "Autobidding with Constraints", WINE 2019, Lecture Notes in Computer Science (2019). https://doi.org/10.1007/978-3-030-35389-6_2
    3. Santiago R. Balseiro, Kshipra Bhawalkar, Zhe Feng, Haihao Lu, Vahab Mirrokni, Balasubramanian Sivan and Di Wang, "A Field Guide for Pacing Budget and ROS Constraints" (arXiv, 16 February 2023, revised 15 December 2023; ICML 2024). https://arxiv.org/abs/2302.08530
    4. Rohan Garg, Yongjin Xiao, Jason (Dianxia) Yang and Mandar Rahurkar, "Smart Fast Finish: Preventing Overdelivery via Daily Budget Pacing at DoorDash" (arXiv, 9 September 2025). https://arxiv.org/abs/2509.07929
    5. Sreeja Apparaju, Yichuan Niu and Xixi Qi, "Feedback Control for Small Budget Pacing" (arXiv, 29 September 2025, revised 9 March 2026). https://arxiv.org/abs/2509.25429
    6. Topsort documentation, "Pacing" (accessed 9 November 2026). https://docs.topsort.com/knowledge-base/ad-server/auctions/pacing/
    7. Lihong Li, Wei Chu, John Langford and Xuanhui Wang, "Unbiased Offline Evaluation of Contextual-bandit-based News Article Recommendation Algorithms" (arXiv, 31 March 2010; WSDM 2011). https://arxiv.org/abs/1003.5956
    8. Min Liu, Jialiang Mao and Kang Kang, "Trustworthy Online Marketplace Experimentation with Budget-split Design" (arXiv, 16 December 2020). https://arxiv.org/abs/2012.08724
    9. Renato Paes Leme, Georgios Piliouras, Jon Schneider, Kelly Spendlove and Song Zuo, "Complex Dynamics in Autobidding Systems" (EC 2024, 8 July 2024). https://doi.org/10.1145/3670865.3673551