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Intelligent reflecting surfaces (IRS) consist of configurable meta-atoms, which can alter the wireless propagation environment through design of their reflection coefficients. We consider adaptive IRS control in the practical setting where (i) the IRS reflection coefficients are attained by adjusting tunable elements embedded in the meta-atoms, (ii) the IRS reflection coefficients are affected by the incident angles of the incoming signals, (iii) the IRS is deployed in multi-path, time-varying channels, and (iv) the feedback link from the base station (BS) to the IRS has a low data rate. Conventional optimization-based IRS control protocols, which rely on channel estimation and conveying the optimized variables to the IRS, are not practical in this setting due to the difficulty of channel estimation and the low data rate of the feedback channel. To address these challenges, we develop a novel adaptive codebook-based limited feedback protocol to control the IRS. We propose two solutions for adaptive IRS codebook design: (i) random adjacency (RA), which utilizes correlations across the channel realizations, and (ii) deep neural network policy-based IRS control (DPIC), which is based on a deep reinforcement learning. Numerical evaluations show that the data rate and average data rate over one coherence time are improved substantially by the proposed schemes.