  Learning to play optimally against any mixture over a diverse set of
strategies is of important practical interests in competitive games. In this
paper, we propose simplex-NeuPL that satisfies two desiderata simultaneously:
i) learning a population of strategically diverse basis policies, represented
by a single conditional network; ii) using the same network, learn
best-responses to any mixture over the simplex of basis policies. We show that
the resulting conditional policies incorporate prior information about their
opponents effectively, enabling near optimal returns against arbitrary mixture
policies in a game with tractable best-responses. We verify that such policies
behave Bayes-optimally under uncertainty and offer insights in using this
flexibility at test time. Finally, we offer evidence that learning
best-responses to any mixture policies is an effective auxiliary task for
strategic exploration, which, by itself, can lead to more performant
populations.
