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Real-time bidding (RTB) is an important mechanism in online display advertising, where a proper bid for each page view plays an essential role for good marketing results. Budget constrained bidding is a typical scenario in RTB where the advertisers hope to maximize the total value of the winning impressions under a pre-set budget constraint. However, the optimal bidding strategy is hard to be derived due to the complexity and volatility of the auction environment. To address these challenges, in this paper, we formulate budget constrained bidding as a Markov Decision Process and propose a model-free reinforcement learning framework to resolve the optimization problem. Our analysis shows that the immediate reward from environment is misleading under a critical resource constraint. Therefore, we innovate a reward function design methodology for the reinforcement learning problems with constraints. Based on the new reward design, we employ a deep neural network to learn the appropriate reward so that the optimal policy can be learned effectively. Different from the prior model-based work, which suffers from the scalability problem, our framework is easy to be deployed in large-scale industrial applications. The experimental evaluations demonstrate the effectiveness of our framework on large-scale real datasets., Comment: In The 27th ACM International Conference on Information and Knowledge Management (CIKM 18), October 22-26, 2018, Torino, Italy. ACM, New York, NY, USA, 9 pages