Memory has become a standard substrate for self-evolving agents, yet retaining experience is not the same as learning how to evolve through it. Existing memory agents can store trajectories, retrieve reflections, or accumulate skills, but often lack the holistic competence to select useful experience, act on it, write reusable knowledge, and maintain a growing repository. We introduce OPD-Evolver, a slow-fast co-evolution framework that cultivates such an agent evolver through on-policy self-distillation. In the fast loop, OPD-Evolver interacts with a four-level memory hierarchy to read, use, write, and maintain experience for rapid test-time evolution. In the slow loop, outcome-calibrated memory attribution and privileged hindsight distill these four abilities into the deployable policy. Across multi-domain benchmarks, OPD-Evolver surpasses memory systems such as ReasoningBank by up to 11.5 points, and training-based methods such as Complementary RL by ~6.45 on average. Further analysis shows that OPD-Evolver internalizes high-value experience and memory management, enabling OPD-Evolver-9B to challenge giant counterparts such as Qwen3.5-397B-A17B and Step-3.5-Flash, pointing beyond memory-augmented agents toward genuinely qualified agent evolvers.

Cold-start supervised fine-tuning (SFT) is a critical initialization step before reinforcement learning from verifiable rewards (RLVR). Yet existing cold-start data selection methods largely inherit criteria from supervised instruction tuning—sample quality, difficulty, perplexity, or diversity—implicitly assuming that a stronger SFT warm start is also a better starting point for RL. We argue that this assumption does not always hold in the SFT-to-RL pipeline: cold-start SFT not only reduces supervised loss but also shapes the initial update geometry that downstream reward optimization inherits. Building on this observation, we propose RL-Proxy-Coverage. Our method estimates a low-rank, reward-relevant gradient subspace from a small set of representative RL anchor prompts and verifier rewards, and selects, as the cold-start subset, those candidate SFT examples whose gradients provide non-redundant coverage of this subspace. In controlled mathematical-reasoning experiments, RL-Proxy-Coverage outperforms representative SFT-centric, hard-diverse, and reward-aware baselines at the early-to-mid RL checkpoints. Our findings suggest a new view of cold-start data: it should be regarded not merely as supervised examples for improving SFT, but as an initialization resource that shapes the starting point of downstream reward optimization.