Large language models excel at a variety of language tasks when prompted with examples or instructions. Yet controlling these models through prompting alone is limited. Tailoring language models through fine-tuning (e.g., via reinforcement learning) can be effective, but it is expensive and requires model access. We propose Inference-time Policy Adapters (IPA), which efficiently tailors a language model such as GPT-3 without fine-tuning it. IPA guides a large base model during decoding time through a lightweight policy adaptor trained to optimize an arbitrary user objective with reinforcement learning. On five challenging text generation tasks, such as toxicity reduction and open-domain generation, IPA consistently brings significant improvements over off-the-shelf language models. It outperforms competitive baseline methods, sometimes even including expensive fine-tuning. In particular, tailoring GPT-2 with IPA can outperform GPT-3, while tailoring GPT-3 with IPA brings a major performance boost over GPT-3 (and sometimes even over GPT-4). Our promising results highlight the potential of IPA as a lightweight alternative to tailoring extreme-scale language models.