$C^3$: COMPETITIVE CONTEXT COMPRESSION FOR LONG-HORIZON AGENTS

Long-horizon language-model agents must compress growing interaction histories while retaining information needed for future decisions. We observe sublinear growth in total response length when an LLM handles several items jointly, suggesting an implicit soft output budget. We introduce Competitive Context Compression ($C^3$), which uses this behavior to induce competition among jointly compressed histories. Because task-reward training does not reliably preserve this implicit budget, $C^3$ regularizes their combined memory length through a validity bonus alongside downstream task success. Over-budget outputs are truncated and receive no validity bonus or partial validity credit; truncation may also reduce task rewards. Individual memories have no fixed quotas. We formulate training over compaction events at multiple depths and use a curriculum to introduce histories shaped by earlier memory decisions. Evaluation on SWE-bench Verified and BrowseComp-Plus shows that the benefits persist when the compressor processes one history at a time: $C^3$ improves task success over single-history GRPO in both domains and reduces cumulative downstream-agent input in long-document search. Ablations show that joint generation and length regularization contribute together, supporting competition during training as a useful signal for compression within individual agent trajectories.