We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two and three dimensions. We show that this scheme allows microswimmers to find nontrivial paths, which enable them to reach a target on average in less time than a naïve microswimmer, which tries, at any instant of time and at a given position in space, to swim in the direction of the target. We use pseudospectral direct numerical simulations of the two- and three-dimensional (incompressible) Navier-Stokes equations to obtain the turbulent flows. We then introduce passive microswimmers that try to swim along a given direction in these flows; the microswimmers do not affect the flow, but they are advected by it. Two nondimensional control parameters play important roles in our learning scheme: (a) the ratio V[over ̃]_{s} of the microswimmer's bare velocity V_{s} and the root-mean-square (rms) velocity u_{rms} of the turbulent fluid and (b) the product B[over ̃] of the microswimmer-response time B and the rms vorticity ω_{rms} of the fluid. We show that the average time required for the microswimmers to reach the target, by using our adversarial-reinforcement learning scheme, eventually reduces below the average time taken by microswimmers that follow the naïve strategy.