Most keyframe selection studies focus on offline settings, assuming access to the full video and query in advance. In contrast, real-world streaming scenarios require online frame selection under unknown video duration, without access to either the query or future frames during selection. To address this, we introduce Streaming Video Memory (SVMem), a compact and representative memory of previously observed content, updated continuously as the video stream unfolds. Building on this setting, we propose the Streaming Video Memory Agent (SVMemAgent), which dynamically maintains a memory by deciding at each timestep whether to replace an existing memory frame with the incoming frame or discard it. SVMemAgent is trained using Group Relative Policy Optimization (GRPO) with task-driven rewards derived from diverse question-answer pairs, implicitly exposing the policy to a distribution of queries during training so that SVMem retains generally informative frames at inference, when queries are unavailable. Experiments on both online and offline video benchmarks show that SVMemAgent consistently outperforms online frame selection baselines and achieves competitive performance with offline methods that assume access to the full video and query. Through task-driven rewards, SVMemAgent learns an emergent keyframe selection policy that prefers frames containing textual information, which may benefit downstream VideoQA tasks.

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