We present a novel confidence- and margin-based discriminative training approach for model adaptation of a hidden Markov model (HMM)-based handwriting recognition system to handle different handwriting styles and their variations. Most current approaches are maximum-likelihood (ML) trained HMM systems and try to adapt their models to different writing styles using writer adaptive training, unsupervised clustering, or additional writer-specific data. Here, discriminative training based on the maximum mutual information (MMI) and minimum phone error (MPE) criteria are used to train writer-independent handwriting models. For model adaptation during decoding, an unsupervised confidence-based discriminative training on a word and frame level within a two-pass decoding process is proposed. The proposed methods are evaluated for closed-vocabulary isolated handwritten word recognition on the IFN/ENIT Arabic handwriting database, where the word error rate is decreased by 33% relative compared to a ML trained baseline system. On the large-vocabulary line recognition task of the IAM English handwriting database, the word error rate is decreased by 25% relative.