Auto-bidding is central to computational advertising, where strategies must maximize advertisers' conversion value under economic constraints. It has evolved from rule-based controllers to reinforcement learning and generative methods such as Decision Transformer (DT). Yet these methods increasingly mismatch the prevailing optimized cost-per-X (oCPX) paradigm, which spans heterogeneous scenarios (e.g., registration, purchase), each served by a separate model, leading to fragmented pipelines and underexploring cross-scenario modeling. Inspired by foundation models like LLMs, unifying these oCPX scenarios into one model raises three challenges: multi-objective control, scalable capacity under strict latency, and safe offline policy improvement. We present OneBid, a unified auto-bidding foundation model that learns a reusable backbone from heterogeneous oCPX logs and adapts it to scenario-specific deployments via offline post-training. Building on DT, OneBid extends single Return-to-Go conditioning to two atomic signals, Return-to-Go for conversion value and Cost-to-Go for cost ratio, plus value-aware regularization on next-action prediction. To absorb distributional heterogeneity, we design a sequence-level Mixture-of-Experts architecture, where shared experts encode cross-scenario knowledge and sparsely-routed experts capture scenario-specific patterns at low latency, yielding consistent scaling with model size and data. During post-training, we align the backbone with scenario preferences via Critic-guided Relative Offline Policy optimization (CROP): a learned critic scores candidate actions group-relatively, avoiding the unsafe online exploration of GRPO-style fine-tuning while constraining policy shift to reduce OOD risk. Validated via online A/B tests and fully deployed at Kuaishou, OneBid delivers an overall +2.2% ADVV gain on oCPX Ads, peaking at +13.1% in the ROAS scenario.

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