AI-Generated Bidding (AIGB)

• AI-Generated Bidding (AIGB) is an autonomous system that adapts bidding strategies in dynamic, multi-agent environments using sequential decision-making.
• It employs techniques like deep reinforcement learning, Monte Carlo simulations, and generative diffusion models to overcome uncertainty and optimize performance.
• Empirical results in board games, online auctions, and power markets show significant improvements in revenue, efficiency, and strategic adaptation.

AI-Generated Bidding (AIGB) describes the class of artificial intelligence systems and methodologies designed to autonomously perform, optimize, and adapt bidding strategies in complex, dynamic, and often multi-agent environments. AIGB is foundational across domains, including combinatorial board games, online advertising, power markets, financial auctions, and resource allocation platforms. Modern approaches to AIGB marshal reinforcement learning, deep neural models, generative diffusion processes, and multi-agent algorithms, advancing beyond fixed rules or myopic heuristics to deliver context-sensitive, near-optimal strategies under uncertainty, non-stationarity, and partial observability.

1. Foundations: Bidding as a Sequential, Probabilistic, and Multi-Agent Problem

AIGB formalizes bidding beyond static optimization, casting it as a sequential decision-making problem that is inherently dynamic and interactive. In Richman games and board scenarios (e.g., Bidding Hex), foundational work connects optimal real-valued bidding with the solution of corresponding random-turn games, where the probability $P(G)$ that a player wins a game %%%%1%%%% in random-turn play appears centrally in optimal bid formulas. Richman's paradigmatic result—$R(G) = 1 - P(G)$ and optimal bid $\delta(v) = \frac{1}{2} - L_H$ for Hex—maps the structure of bidding games directly onto probabilistic graphical models and informs the design of efficient sampling-based AIs (0812.3677).

In auction and advertising contexts, AIGB frequently leverages the Markov Decision Process (MDP) or generalizations thereof. Here, the environment's state (system configuration, budget, inventory, history) evolves across timesteps as agents adjust their bidding actions based on observations and possibly internal goals. Bidding is thus recast as a trajectory generation or planning problem over action-state sequences, where the AI must anticipate the effect not only of its next move but of entire action trajectories on eventual revenue, utility, or other performance metrics.

2. Algorithmic Advances: From Reinforcement Learning to Generative Models

AIGB systems have evolved along several algorithmic axes:

• Monte Carlo and Probabilistic Simulation: In Bidding Hex and related games, large-scale Monte Carlo simulation is used to estimate the “criticality” of board positions and to determine near-optimal moves and bids without enumerating all possibilities. For a partially filled Hex board, hundreds of thousands of random completions can be sampled per move, yielding empirical $L_H$ statistics that precisely guide bidding decisions (0812.3677).
• Deep Reinforcement Learning (DRL): DRL frameworks dominate in complex environments, such as bridge bidding (Yeh et al., 2016, Rong et al., 2019, Kita et al., 14 Jun 2024), Doudizhu (Lei et al., 14 Jul 2024), advertising (Guo et al., 25 May 2024), and power markets (Liu et al., 15 Oct 2024). Q-learning variants—with deep neural networks approximating value or Q-functions—handle nonlinearity and vast combinatorial state spaces. Layered, decentralized architectures manage the sequential and partner-conditional structure of games like bridge (Yeh et al., 2016).
• Generative Modeling (Transformers, Diffusion): Motivated by the limitations of stepwise RL in long-horizon and non-Markovian domains, recent AIGB systems employ trajectory-level generative models. Conditional diffusion models (e.g., DiffBid) stochastically sample or complete full sequences of system states or actions, directly conditioning on desired returns or constraints and bypassing error accumulation typical in MDPs (Guo et al., 25 May 2024, Li et al., 3 Sep 2025). Decision Transformers leverage sequential data to auto-regressively predict bid actions by conditioning on historical context and future objectives (Li et al., 22 Dec 2024, Gao et al., 20 Apr 2025).
• Expert-guided and Hybrid Architectures: Some frameworks employ trajectories generated by expert systems, human annotation, or theoretical optima to bootstrap or guide AIGB model training, especially when logged real-world data is noisy or sparse (Li et al., 22 Jul 2025). PU (Positive-Unlabeled) discriminators, bagged reward redistribution, and expert-guided inference mitigate reward sparsity and suboptimal data.

3. Models, Mathematical Formulations, and Optimization Objectives

Key mathematical and algorithmic constructs in AIGB include:

• Move and Bid Valuation in Games: Optimal move/bid selection in bidding games utilizes empirical estimates $L_H$ (probabilities that an open Hex is filled with the losing color), yielding the bid formula:

$\delta(v) = \frac{1}{2} - L_H$

and for discrete chips $$b = \lfloor (1/2 - L_H) \cdot \text{total chips} \rfloor$$ (0812.3677).

• BeLLMan Equations and Policy Update: DRL approaches employ BeLLMan-style updates for action-value functions $Q(s, a)$, often regularized to prevent overestimation in multi-step sequential environments:

$$Q^*(s, a) = \mathbb{E}_{s'} [r + \gamma \max_{a'} Q^*(s', a') | s, a ]$$

with squared-error losses or penetrative extensions (Yeh et al., 2016).

• Generative Trajectory Modeling: Diffusion models add Gaussian noise to trajectories in forward steps, then iteratively denoise with conditional guidance to match targets:

$$q(x_k | x_{k-1}) = \mathcal{N}(x_k; \sqrt{1-\beta_k} x_{k-1}, \beta_k I)$$

and

$$\hat{\epsilon}_k := \epsilon_\theta( x_k, k ) + \omega ( \epsilon_\theta(x_k, y, k) - \epsilon_\theta(x_k, k) ).$$

The model is trained to maximize the trajectory likelihood conditioned on objectives (Guo et al., 25 May 2024, Li et al., 3 Sep 2025).

• Policy Optimization in Auctions: In online auctions, parameterized policies (Bid Nets) are trained to be monotonic and individually rational, leveraging pseudo-gradient (PG) methods that incorporate predictions of opponents’ reactions (Hu et al., 2022). Group Relative Policy Optimization (GRPO) uses group-based advantage estimates and KL penalties for stable policy updates in surplus maximization (Huang et al., 6 Aug 2025).

4. Empirical Performance, Evaluation, and Deployment

AIGB systems have been validated across a wide array of simulated and industrial settings:

• Board Games: Monte Carlo AIGB for Bidding Hex performs hundreds of thousands of simulations per move, yielding moves and bids indistinguishable from theoretical optima for boards up to $11 \times 11$, and consistently defeating strong human opponents (0812.3677).
• Bridge/Bidding Card Games: Deep RL models achieve test costs (International Match Points, IMPs) lower than champion human-designed programs (e.g., WBridge5), with end-to-end feature extraction enabling robust performance under partial information (Yeh et al., 2016, Kita et al., 14 Jun 2024). RL-enhanced models integrated with policy optimization and self-play set new baselines in cooperative, multi-agent settings (Kita et al., 14 Jun 2024).
• Online Advertising and Auctions: Generative trajectory-based methods (DiffBid, GAS, GAVE, AIGB-Pearl, CBD) consistently outperform RL and behavioral cloning baselines, with improvements in cumulative reward (0.65–8%), GMV (2.81–4.7%), ROI (+3.36%), and target metric increments (up to 4.60%) in both synthetic and real-world (Alibaba, Kuaishou, Meituan, TaoBao) deployments (Guo et al., 25 May 2024, Li et al., 22 Dec 2024, Li et al., 3 Sep 2025, Mou et al., 19 Sep 2025, Gao et al., 20 Apr 2025).
• Complex Power Markets and BESS: RL agents with high-dimensional bid representations and risk-augmentation (e.g., CVaR-constrained PPO) substantially improve profits, adaptability, and operational risk profiles for storage systems providing frequency reserves or FCAS services. LLM-assisted decision frameworks further enhance strategy robustness in non-stationary environments (Liu et al., 15 Oct 2024, Zhang et al., 3 Jun 2024, Kempitiya et al., 2021).

5. Notable Methodological Innovations

Recent AIGB literature introduces several distinctive methodological advances:

• Diffusion Completer-Aligner (CBD): Augments diffusion training with random truncations to ensure dynamic legitimacy of trajectory completions, followed by trajectory-level return alignment via gradient-based refinement (Li et al., 3 Sep 2025).
• Reward Preference Alignment Systems and GRPO: GBS frameworks fuse policy gradient updates with group-based surplus optimization, exploration-utility entropy regularization, and post-training reward model guidance, enabling direct, tokenized generation of bid shading ratios in RTB (Huang et al., 6 Aug 2025).
• Offline Evaluation and Non-Bootstrapped Policy Search: Trajectory evaluators with LLM-based architectural enhancements, hybrid point/pairwise loss, and integration of expert rules yield more stable, reliable reward assignments for planner optimization. Policy updates are conservative, penalizing divergence from observed data while pursuing quality improvement (Mou et al., 19 Sep 2025).
• Expert-Guided PU Learning and Bagged Rewards: PU discriminators identify expert-like transitions in suboptimal logs, and “bags” of transitions smooth sparse, binary reward signals, significantly improving convergence and reliability in EBaReT (Li et al., 22 Jul 2025).
• LLMs as Auction Participants and Assistants: LLMs exhibit human-like (risk-averse, sometimes bounded rational) behavior in controlled synthetic auction environments, matching empirical observations from behavioral economics and suggesting further potential as both experimental tools and symbolic agents (Shah et al., 12 Jul 2025). Separately, LLMs serve as agents for market analysis, hybrid decision-making, and interpretability within DRL bidding frameworks (Zhang et al., 3 Jun 2024).

6. Open Challenges and Future Directions

Despite substantial progress, several challenges remain prominent in AIGB research:

• Quality of Offline Data and OOD Actions: Generative models are susceptible to the limitations of their training logs; offline behavioral collapse and unwanted policy drift in uncharted action space are recurrent bottlenecks. Value-guided or discriminative critics, conservative learning objectives, and explicit risk/constraint benchmarking are active research directions (Gao et al., 20 Apr 2025, Li et al., 22 Jul 2025, Mou et al., 19 Sep 2025).
• Dynamic Legitimacy, Explainability, and Planning: Ensuring that generated trajectories respect temporal and physical consistency, especially in high-frequency or high-noise domains, requires innovations in sequence completion and trajectory refinement (e.g., diffusion completer-aligner techniques (Li et al., 3 Sep 2025)).
• Efficient Adaptation and Scalability: Post-training search, online fine-tuning, scalable model distillation, and open-source baselines are increasingly emphasized to enable robust deployment and rapid experimentation for industry scenarios (Li et al., 22 Dec 2024, Kita et al., 14 Jun 2024).
• Multi-objective and Multi-agent Bidding: Real-world AIGB must balance revenue, fairness, market liquidity, and regulatory requirements. Increased attention to personalized constraints, responsive adaptation to market regimes (e.g., budget, ROI, regulation), and integration with truthful or incentive-compatible auction design is expected (Xing et al., 2023).

7. Cross-Domain Applicability and Generalization

The AIGB paradigm extends well beyond individual games or verticals. Compact representations for high-dimensional, sequential action histories, inference and integration of hidden state estimates (e.g., partner hand in bridge, future market states in auctions), and the unification of generative planning with explicit evaluators support migration to domains such as poker, mahjong, power system markets, and online resource allocation. As large foundation models and generative AI architectures mature, AIGB is expected to underpin next-generation autonomous agents for economic, strategic, and societal-scale decision problems.