【问题】代码中迭代收敛cost近似的疑惑

[freeclouds]

你好，请教一下，我在分析代码过程中对于前向过程中和后向过程中对于cost下降的近似，下面两段代码不是很理解，这个近似的原理是什么呀，

        if (i < _num_steps - 1) {
            _approx_cost_decay_info.first += _k.at(i).transpose() * qu;
            _approx_cost_decay_info.second += (0.5 * _k.at(i).transpose() * quu * _k.at(i))(0);
        }

        const double approx_cost_decay = -(alpha * _approx_cost_decay_info.first + alpha * alpha * _approx_cost_decay_info.second);
        LOG(INFO) << "[Forward pass] Iter " << _iter << ", alpha " << alpha << ", actual cost decay " << actual_cost_decay << ", approx " << approx_cost_decay;