This paper introduces a rate-based nonlinear neural network in which excitatory (E) neurons receive feedforward excitation from sensory (S) neurons, and inhibit each other through disynaptic pathways mediated by inhibitory (I) interneurons. Correlation-based plasticity of disynaptic inhibition serves to incompletely decorrelate E neuron activity, pushing the E neurons to learn distinct sensory features. The plasticity equations additionally contain "extra" terms fostering competition between excitatory synapses converging onto the same postsynaptic neuron and inhibitory synapses diverging from the same presynaptic neuron. The parameters of competition between S$\to$E connections can be adjusted to make learned features look more like "parts" or "wholes." The parameters of competition between I-E connections can be adjusted to set the typical decorrelatedness and sparsity of E neuron activity. Numerical simulations of unsupervised learning show that relatively few I neurons can be sufficient for achieving good decorrelation, and increasing the number of I neurons makes decorrelation more complete. Excitatory and inhibitory inputs to active E neurons are approximately balanced as a result of learning.