Basic Allowance for Housing Calculation Improvement Act of 2023 This bill requires the Department of Defense to seek to enter into an agreement with an entity to calculate the monthly basic allowance for housing rates for members of the uniformed services in at least 15 military housing areas. Under the bill, the entity must be a nationally recognized entity in the field of single-family housing that has data on local rental rates in real estate markets across the United States. Additionally, the entity must use industry standard machine learning and artificial intelligence algorithms in its calculations.