Human capability to anticipate near future from visual observations and non-verbal cues is essential for developing intelligent systems that need to interact with people. Several research areas, such as human-robot interaction (HRI), assisted living or autonomous driving need to foresee future events to avoid crashes or help people. Egocentric scenarios are classic examples where action anticipation is applied due to their numerous applications. Such challenging task demands to capture and model domain's hidden structure to reduce prediction uncertainty. Since multiple actions may equally occur in the future, we treat action anticipation as a multi-label problem with missing labels extending the concept of label smoothing. This idea resembles the knowledge distillation process since useful information is injected into the model during training. We implement a multi-modal framework based on long short-term memory (LSTM) networks to summarize past observations and make predictions at different time steps. We perform extensive experiments on EPIC-Kitchens and EGTEA Gaze+ datasets including more than 2500 and 100 action classes, respectively. The experiments show that label smoothing systematically improves performance of state-of-the-art models for action anticipation.