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PROteolysis TArgeting Chimeras (PROTACs) are an emerging therapeutic modality for degrading a protein of interest (POI) by marking it for degradation by the proteasome. Recent developments in artificial intelligence (AI) suggest that deep generative models can assist with the de novo design of molecules with desired properties, and their application to PROTAC design remains largely unexplored. We show that a graph-based generative model can be used to propose novel PROTAC-like structures from empty graphs. Our model can be guided towards the generation of large molecules (30--140 heavy atoms) predicted to degrade a POI through policy-gradient reinforcement learning (RL). Rewards during RL are applied using a boosted tree surrogate model that predicts a molecule's degradation potential for each POI. Using this approach, we steer the generative model towards compounds with higher likelihoods of predicted degradation activity. Despite being trained on sparse public data, the generative model proposes molecules with substructures found in known degraders. After fine-tuning, predicted activity against a challenging POI increases from 50% to >80% with near-perfect chemical validity for sampled compounds, suggesting this is a promising approach for the optimization of large, PROTAC-like molecules for targeted protein degradation.