We study distributed algorithms for adjusting beam-forming vectors and receiver filters in multiple-input multiple-output (MIMO) interference networks, with the assumption that each user uses a single beam and a linear filter at the receiver. In such a setting there have been several distributed algorithms studied for maximizing the sum-rate or sum-utility assuming perfect channel state information (CSI) at the transmitters and receivers. The focus of this paper is to study adaptive algorithms for time-varying channels, without assuming any CSI at the transmitters or receivers. Specifically, we consider an adaptive version of the recent Max-SINR algorithm for a time-division duplex system. This algorithm uses a period of bi-directional training followed by a block of data transmission. Training in the forward direction is sent using the current beam-formers and used to adapt the receive filters. Training in the reverse direction is sent using the current receive filters as beams and used to adapt the transmit beamformers. The adaptation of both receive filters and beamformers is done using a leastsquares objective for the current block. In order to improve the performance when the training data is limited, we also consider using exponentially weighted data from previous blocks. Numerical results are presented that compare the performance of the algorithms in different settings.