We propose a new mechanism to accurately answer a user-provided set of linear\ncounting queries under local differential privacy (LDP). Given a set of linear\ncounting queries (the workload) our mechanism automatically adapts to provide\naccuracy on the workload queries. We define a parametric class of mechanisms\nthat produce unbiased estimates of the workload, and formulate a constrained\noptimization problem to select a mechanism from this class that minimizes\nexpected total squared error. We solve this optimization problem numerically\nusing projected gradient descent and provide an efficient implementation that\nscales to large workloads. We demonstrate the effectiveness of our\noptimization-based approach in a wide variety of settings, showing that it\noutperforms many competitors, even outperforming existing mechanisms on the\nworkloads for which they were intended.\n