Fine-tuning large language models (LLMs) on downstream tasks requires substantial computational resources. Selective PEFT, a class of parameter-efficient fine-tuning (PEFT) methodologies, aims to mitigate these computational challenges by selectively fine-tuning only a small fraction of the model parameters. Although parameter-efficient, these techniques often fail to match the performance of fully fine-tuned models, primarily due to inherent biases introduced during parameter selection. Traditional selective PEFT techniques use a fixed set of parameters selected using different importance heuristics, failing to capture parameter importance dynamically and often leading to suboptimal performance. We introduce $\text{ID}^3$, a novel selective PEFT method that calculates parameter importance continually, and dynamically unmasks parameters by balancing exploration and exploitation in parameter selection. Our empirical study on 16 tasks spanning natural language understanding, mathematical reasoning and summarization demonstrates the effectiveness of our method compared to fixed-masking selective PEFT techniques. We analytically show that $\text{ID}^3$ reduces the number of gradient updates by a factor of two, enhancing computational efficiency. Since $\text{ID}^3$ is robust to random initialization of neurons and operates directly on the optimization process, it is highly flexible and can be integrated with existing additive and reparametrization-based PEFT techniques such as adapters and LoRA respectively.