Large language models (LLMs) achieve strong performance when all task-relevant information is available upfront, as in static prediction and instruction-following problems. However, many real-world decision-making tasks are inherently online: crucial information must be acquired through interaction, feedback is delayed, and effective behavior requires balancing information collection and exploitation over time. While in-context learning enables adaptation without weight updates, existing LLMs often struggle to reliably leverage in-context interaction experience in such settings. In this work, we show that this limitation can be addressed through training. We introduce ORBIT, a multi-task, multi-episode meta-reinforcement learning framework that trains LLMs to learn from interaction in context. After meta-training, a relatively small open-source model (Qwen3-14B) demonstrates substantially improved in-context online learning on entirely unseen environments, matching the performance of GPT-5.2 and outperforming standard RL fine-tuning by a large margin. Scaling experiments further reveal consistent gains with model size, suggesting significant headroom for learn-at-inference-time decision-making agents. Code reproducing the results in the paper can be found at https://github.com/XiaofengLin7/ORBIT.