Semantic caching lowers the cost of serving large language models (LLMs) by reusing stored responses for similar requests. In multi-turn conversations, whether a cached response is acceptable depends on both conversations' histories, which embedding similarity of requests and histories predicts poorly (AUC 0.62--0.74 on five workloads). We therefore learn the \emph{reuse risk}, the probability that a cached response is unacceptable, from judge feedback, and choose a budgeted set of conversation states to cache by weighing the generation cost a reuse avoids against a price for unacceptable reuse. We propose CUCB-SC-MT, which learns a cache from logged conversations with a suboptimality guarantee, and CLCB-LS-MT, which learns online and has $\tilde O(\sqrt N)$ regret over $N$ requests when conversation states recur. On math-tutoring (SocraTeach) and movie-ticketing (Taskmaster-3) conversations, both achieve lower loss than prior semantic caching approaches: ContextCache, multi-turn variants of ElastiCache and vCache, and single-turn semantic caching at every cache budget. With 1,000 cache entries, CLCB-LS-MT avoids 35--41\% of the generation cost through acceptable reuses, against at most 22--25\% for the baselines, and lowers estimated serving latency by 19--35\%.

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