Semantic parsing from denotations faces two key challenges in model training: (1) given only the denotations (e.g., answers), search for good candidate semantic parses, and (2) choose the best model update algorithm. We propose effective and general solutions to each of them. Using policy shaping, we bias the search procedure towards semantic parses that are more compatible to the text, which provide better supervision signals for training. In addition, we propose an update equation that generalizes three different families of learning algorithms, which enables fast model exploration. When experimented on a recently proposed sequential question answering dataset, our framework leads to a new state-of-theart model that outperforms previous work by 5.0% absolute on exact match accuracy.