Window aggregates are ubiquitous in stream processing. In Azure Stream Analytics (ASA), a stream processing service hosted by Microsoft's Azure cloud, we see many customer queries that contain aggregate functions (such as MIN and MAX) over multiple correlated windows (e.g., tumbling windows of length five minutes and ten minutes) defined on the same event stream. In this paper, we present a cost-based optimization framework for optimizing such queries by sharing computation among multiple windows. In particular, we introduce the notion of factor windows, which are auxiliary windows that are not in the input query but may nevertheless help reduce the overall computation cost, and our cost-based optimizer can produce rewritten query plans that have lower costs than the original query plan by utilizing factor windows. Since our optimization techniques are at the level of query (plan) rewriting, they can be implemented on any stream processing system that supports a declarative, SQL-like query language without changing the underlying query execution engine. We formalize the shared computation problem, present the optimization techniques in detail, and report evaluation results over both synthetic and real datasets. Our results show that, compared to the original query plans, the rewritten plans output by our cost-based optimizer can yield significantly higher (up to 16.8x) throughput.