Digital Microfluidic Biochips (DMFBs), used in various kinds of fields like DNA analysis, clinical diagnosis, and PCR testing, have made biochemical experiments more compact, efficient, and user-friendly than previous ways. However, their reliability is often compromised by their inability to adapt to all kinds of errors. All errors in biochips can be categorized into two types: known errors and unknown errors. Known errors are detectable before the start of the routing process through sensors or cameras. Unknown errors, in contrast, become apparent only during the routing process and remain undetected by sensors or cameras, which is the biggest issue to unexpectedly stop the routing process and diminishes the reliability of biochips. This paper introduces a deep reinforcement learning-based routing algorithm designed to manage not only known errors but also unknown errors. Our experiments demonstrate that our algorithm outperforms previous ones in terms of the success rate of the routing in the scenario including both known errors and unknown errors. Additionally, our algorithm contributes to detecting unknown errors during the routing process and identifying the most efficient routing path with high probability.